First thing - if you're shooting reversal, then it's not negative. It's a positive image. What's in the camera is what you're editing and projecting. The traditional workflow using neg would be to shoot negative, have a workprint made, then go back to the negative to cut it to match the final edit. From this, you'd strike your prints. In this scenario, the workprint is kind of sacrificial, because it will be handled quite a bit and every time the film is exposed to air, it's likely to pick up dust. You'll probably see a fair bit of dust and some small scratching, even if you're careful, at each cut you make.
I would suggest that a better workflow would be to shoot the film and then scan it and edit digitally. Don't even project the film - go direct from processing to scanner, and you should get a pretty pristine looking scan. Any time the film is run through a projector, viewer, or even unspooled to look at by eye, you risk getting it dirty. That's why the old neg/workprint/neg cut workflow worked - the only times the negative were ever handled were when the film was shot, the film was processed and workprinted, and when the neg was cut to match the final edit. As a result, you ensured that any subsequent prints looked good. The same idea applies to hybrid film/digital workflows: handle the film as minimally as possible, and scan early.
All that said, if you need to do this manually, don't run it through a projector, get yourself a simple Moviescop (or similar) viewer, sync block and rewinds on ebay. Set up a on a very clean bench, and be extra careful about how you handle the film. While presstape-style splices are fine, they're kind of a pain. If you can afford it, get a guillotine style splicer. Fewer fingerprints on the tape that way, and they're way faster to work with.