How do I keep smallest gear on my crank shaft from contacting frame
Welcome to BB standards hell...... you are about to learn far more than you wanted to about bicycle gearing cranks and chain rings.....The only spec I could find on these was the 1999 model, which used a Shimano BB-UN52, 113mm spindle BB Shell Width   73mm - its pretty common and typical of that era MTB. 

Your idea of another crank set is a possible solution, that might be easier if you have a supply of donor bikes, is a larger small chain ring. 

Its likely though you need a longer bottom bracket spindle, as a short spindle will not only cause this to be a problem, but will affect the chain line. With incorrect chain-line you may have problems with getting gear shifts to work smoothly and reliably, and have problems with chain drops.  Read up about chain line Here (as always, Sheldon Brown)

Presuming its square taper BB, they come in a range of lengths. You should be able to measure your current length, and might find a longer one on your donor bikes. Hopefully the one you have now is around 106mm, meaning all you need to do is source the correct 113mm sized one.