You can change the computer attached to a timer whenever you like. It has nothing to do with the times. I would print the net times off the timer and verify every time was correct for that run in whatever software you were using to do data processing to make sure I didn't miss any times. This is a good process you don't see commonly happen anymore.
emember, there is no rule you must even have 1 computer connected to the timers, let alone 2 or 3. I only run one computer connected to a timer in general and haven't lost a computer in the middle of the race in a few years though I have heard it happens occasionally. No big deal if it does, restart, and keep going, no need to even stop the race. Just add the few net times that weren't sent to the software while the computer was down, or if your timer doesn't calculate net times, just calcualte them or add the TODs to the software (in SST's case)or to whatever software you are running and let it calculate the net times.
Jenna