Imho historically accurate “lockpicking” can be fun as well. You need to acquire some sort of master key. Steal it or make it. Steal it is easy, just rob or punch to head some keymaster or someone that can have it.
But to make master key you need at least go to NPC that creates locks and keys, I can imagine there can be always someone for each location (lets say one under each knight or baron). You can try to persuade him or his student or family member to help you out. Or steal master key from him. You can “level up” with each NPC that make keys and locks (lets call him for now keymaker:)" and levels can be measured by his opinion of you so at lvl0 he gives you nothing. At lvl1 he gives you let’s say simple master key to common folks chests. At lvl2 he gives you master key from some doors around, and with the highest level possible you will get ultimate master key to everything in the area.
Or if you dont want to loose time with keymaker, simply punch keymaker to the head and take master key
also you dont have to loose time with keys at all, just open the lock with brute force!
Thats just few ideas how it can be done IMHO 