1999 camry ce 4-cyl water pump?

I had my water pump/timing belt replaced about 5 years ago at around
60K miles, my current OD is 95K. There's an issue with my 2nd water
pump and it needs to be replaced. My mechanic says he needs to remove/
replace  the timing belt too ($500+ total).
The pump is in a convenient place/orientation and it seems like it
should be easy to tension the existing belt (even a rope tied to the
front frame near the radiator would probably work), remove the water
pump, replace the water pump, without removing and replacing the
timing belt.  My mechanic says this can't be done. I find this hard to
believe, is this true, or is trying this a bad idea?