If the compressor is making nose when your A/C is not engaged, then yes, you could do this, but the problem is probably not so bad. You may be able to replace the A/C clutch assembly for cheap.
If the compressor is only making noise when the A/C *is* engaged (ie cooling) then the answer is a lot easier, just stop using A/C, or if you like, unplug one of the wires going to the compressor clutch. (the part at the front of the compressor where the pulley is attached)
When the electric compressor clutch is disengaged, the pulley spins freely. When the clutch is engaged, it actually connects the shaft of the compressor and that's what will take power away.
If it is making noise ALL of the time, that means the fault isn't in the compressor itself (expensive) but is in the clutch/pulley assembly (cheap).
You COULD go the belt route, but remember that your A/C doesn't just cool the car, it also dehumidifies, so even in the winter it is good to have... (it will kick on when you use your defroster) Also resale value (even of a 97 civic) will hit the floor, better to try to fix it now for $100 then have to figure out all the things that are wrong a few years from now if you never use it.