If you set it up right there shouldn’t be feedback. I would create a group track, use sends on your 4 original tracks to create a mix to send to your reverb. Route the output of the group track to the reverb and record that to a new track.
It depends on your hardware effect how you set this up. For a reverb, ideally you’d want it to output 100% wet, with no original signal. That way you can use your original 4 tracks + the separately recorded reverb track. If your reverb outputs both the reverb and the original signal, then you’ll have to ditch the 4 original tracks after recording your outboard effect, as the output from the reverb will be your final track. If the latter, latency is of no concern because everything is delayed equally. If the former, you might experience some latency which you can easily fix by moving the recorded reverb back a bit in time. record a test signal with a clear transient so you can clearly see what latency you’re looking at.