Get your perception way up. More so than anyone fight, mimics are the biggest threat to your chastity. You effectively need max perception whenever you walk into a chest. I think 7 plus surveyor can let you do this without wasting food to check, but I would need to double check.
Otherwise just a strong combat build should do. Agility is more important than strength, as it effects balance and some weapon damage. Plus it lets you avoid some nasty events. Honestly it is just a matter of saving often enough to try fights where losing ends chastity. Most enemies are easy to figure out with multiple tries.
Once you have some strength, don't be afraid to grapple and throw when you can. It is surprisingly effective at dealing damage while staying safe.