TomD
"First, I had to do a rip cut to square up my boards."

Just to be clear, we are taking about cutting the sides, not the ends, right?

"I had trouble staying on the line and need to figure out how to fix that."

Normally ripping for width one is going to follow up with a plane, so a modest amount of error is no biggie. One issue is how agressive is the saw. A lot of replaceable blade saws have softwood teeth, if you are using a hard wood then they will feel harsh in the cut, and may cause problems. Try some practice on soft wood to see where the issues are.

Notwithstanding what I said earlier, hand strength wise western saws are probably better, overall horsepower wise, Japanese saws are probably better. Most western bodies will probably achieve hold downs easier with western saws. If you have a decent bench, then either can be served. Actually, before you spend a fortune one high end tools, I would recommend getting shop furniture first.

"Second, my left hand is very week from my injury. I had trouble holding my try square and straight edge steady and so my lines were all over the place. Any tips? "

Is this the same operation? Or have we moved on to crosscutting the board? Japanese try squares do sit with a lot less wiggle, and they are light. They have a figure of 8 section to them, so that they sit on two points of the beam, and those points do not skid around. Another thing you can do with any flat square be it Japanese or a framing square, is lie it entirely on the top of the board, then use a fence to the back, possibly a bench hook, for alignment. Having a bench hook/shooting board, will also help with sawing and squaring. Do you have a table saw? Because the fence and table make good reference surfaces for aligning your square.

By the way, are the physical issue you have, made better or worse, over time, by exercise.