Yeah, that's a "danged if you do, danged if you don't" kind of situation.
The best way to remove stress is likely to put him in your reef where he has room to move and things to pick, but you risk exposing your other fish to it.
Were it me, I'd probably risk it, assuming I had a pretty peaceful tank otherwise. Or at least attempt it and if the stress level in the tank spikes, get him out.