Male cat anaesthesia for a neuter is extremely fast. I don't know your vet's procedure but the procedures I've sat in on the cat received a shot of IV anesthetic and was castrated and placed into recovery within 10 minutes, maybe more like 5 even. No ventilator, no shaving, no stitches, just another shot of long acting penicillin to ward off any potential infection, and painkiller.
The risk for anaesthetic definitely does increase with the length and strength of administration, but for a neuter I would not put it off because the risk is fairly minimal. Putting up with the spraying would be much worst... Yuck.