I’ve already had experience using almost entirely slick 38c tyres for long rides both on and off road (Kenda Kwik Tendril, so nothing fancy compound wise). They were absolutely fine, although I wasn’t ragging muddy or loose corners, and did have some small slips when braking on steep grass.
I’ve since upgraded to Vittoria Tereno Dry which are virtually slick in the centre but still have some tread on the shoulders. Have given them a bit more punishment (deliberately leaning into corners, getting waylaid in thick sticky mud etc.) and have great faith in them.
So on that basis, I think you could get away with some that is virtually slick, maybe with some corner knobs. It seems that the lighter slick tyres (Panaracer) seem to have a reputation for punctures, so go with something heavier e.g. in the 500g range for a 38c tyre?