I used a standard 7-1/4 circular saw to regroove my entire deck. I think you could definitely do this with the saw you're talking about (aside from the concerns introduced below). At many of the edges and in the complex areas by the king board at the bow, I had to regroove by hand/use a router.
I'm not sure about the shoe you're talking about. I made a jig by screwing a thin, 4-foot long strip of wood in the middle of a 1-foot by 4-foot sheet of plywood. I then cut the edge of the plywood off using the thin strip as a rail, pushing the base of the circular saw against it as I cut. I then used this jig to cut all of the straight lines on the deck (described in more detail here with pictures: http://www.woodworkersjournal.com/makin ... cular-saw/
). I would first set the jig at the edge of the caulk line, kneel on the back of it (as opposed to clamping it as described in the link), and run the circular saw down the caulk line. For lines that were slightly curved (as in the bow of the 42-MY I have), the circular saw still worked perfectly, but I had to do it freehand. This was no problem, it just took a little bit more time.
It's good to wear a mask for this, because the black caulk dust sucks.
I stacked 3 blades on my circular saw to get the appropriate caulk line width. Blades of different make will have different kerf and slightly different diameter. You can try combing different ones, or bring a caliper to the hardware store. I would highly recommend widening the caulk lines slightly from what is currently there. This ensures that fresh wood will be exposed on both sides of the line. Too thin of a blade stack will leave a thin strip of old caulk attached to at least one side of the new groove - it sucks to have to go back and clean it out. Even with a wider groove, I think it took about the same amount of time for me to regroove as it did to clean out excess black reside (the TDS teak decking hook is amazing for this - buy one, and be ready to sharpen it repeatedly).
I did not use spacers between blades, simply stacked the blades - no problem. I tried many different blades to get the right width. In the end I used three different blades with a different number of teeth - didn't matter at all. Coarse and fine-tooth blades both did a clean job. I found that a groove width of .21-.22 inches worked well for my boat.
The only problem I can see using a battery-powered 3-3/4-inch saw is that spinning up three blades requires a significant amount of torque. Also, stacking three blades requires a spindle that is long enough to accommodate. My Milwaukee had a long enough spindle that three blades stacked still allowed me to thread on the nut with 4-5 threads engaged. You may find that a plug-in saw works better for you. You may also get straighter lines with a larger saw. The best bet is probably to use a larger saw for the open areas, then finish with the 3-3/4 for those areas the large saw can't reach.
To get nice grooves of even depth, it worked best to have a smooth, flat surface to set the circular saw/jig on prior to cutting. Unfortunately, on my deck, some of the old caulk lines were proud of the surface, and some were completely gone. I needed to use a sander to bring all of these lines down flush with the wood surface so I could get consistent groove depths. Many people say to never sand a teak deck, but most of these people would have simply replaced a deck in my condition. Some of my boards were very worn and to get the deck completely smooth I would have to sand a ton of wood off. Instead, I sanded a moderate amount, leaving the extremely worn boards as is. When caulking, this meant I only had to tape the really deep, worn areas so as not to fill damaged boards with caulk. This allowed me to minimize the amount of taping and get a nice-looking finished product without sanding off a huge amount of teak.
This method required two sanding steps. You will either need a belt sander, or to rent a floor sander. A first sanding pass was made to smooth the deck (and more importantly bring flush the proud caulk lines), and a second sanding step was used to remove the new caulk overflow. I pulled the tape off while the deck was still wet, prior to the second sanding step. The smoother, sanded deck sheds water much better than the worn deck. I believe this prevents teak wear because water doesn't sit on the deck, softening the boards.
I also have a different approach for plugging screw holes. Screws are completely unnecessary for a teak deck. They are very helpful for the initial installation, but it's the black adhesive that really holds the teak to the fiberglass. TDS no longer uses screws on many installations, and if you try to pull up your teak deck, even after removing the screws, you will find that it's nearly impossible because the adhesive is so tenacious. I found that my deck was most damaged near screw holes because this was where water was entering. For this reason, I simply removed all of the screws, and drilled holes of 3/8 diameter deep into the fiberglass sub-deck. Then, I filled these up with a syringe of epoxy to a level just above the bottom surface of the wood. This leaves a nice plug of epoxy bonding the wood to the fiberglass. Before this epoxy set, I dipped new teak plugs in epoxy and hammered them in. Without screws in there, the plugs go far deeper, the epoxy is much stronger, and I will never have to do this job again. Use an oscillating tool with a smooth blade to cut off the plugs. Use the plugs sold by jockscotsteve on eBay. They are far cheaper than that whitecap garbage, and they have a beautiful taper that is much easier to insert (I have no affiliation with any vendors mentioned here). Also, the guy combines shipping if you order multiple - a true gentleman.
Also, for those boards that are no longer adhered, you want to sneak some 3M 4000 underneath them. Don't use 4200 or 5200 because teak cleaning products can dissolve them. If you pull up the boards slightly, squirt some 4000 under there and temporarily use a screw with a washer in the groove to hold them down, you can get a nice firm deck again.
Finally, I used TDS SIS-440 to caulk, and Semco to finish the deck. I don't believe a deck as old and worn as mine (30 years without a refinish) can be allowed to continue to weather as badly. Some of my boards were down to 1/4-inch thick in places. I am also against oiling, but Semco gives a nice finish that doesn't look treated, yet allows the water to bead off better, reducing wear. I believe this deck should last 20 more years.
My order of operations was: remove screws, sand, regroove, re-seat boards where necessary with 4000, drill screw holes, fill with epoxy and plug, cut off plugs, clean and sand grooves, tape deep areas, acetone, caulk, remove tape while wet (the sooner the better), sand, wash, treat with semco.