Are we talking flintlock or percussion?
I think you should keep the gun indoors, it will help alot.
I leave mine loaded for 2-3 weeks during hunting season from time to time.
I think in your case, the gun will be more reliable with real blackpowder instead of the triple 7. Out of everything ever made to make a steel barrel go boom, the easiest thing to lite out of all of them is real blackpowder.
I either use smokeless for things that go boom, or if I have to use non-smokeless, it's real blackpowder. Even in modern wiz bang 209 primered ones. I only us my wiz banger 209 as a loaner gun. It has been loaded between mid october until mid december this year and it worked just fine and it's loaded with 90grs of FFFg goex.
A suficiently lubricated patched or grease sealed maxiball will keep the muzzle end high and dry. you may want to considered sealing up the other end, this is where the bigger issue is.
Flintlock with a feather or a rubber cap for a percussion gun.
Might be a rough guess here, but I think the flintlock will stay fresh longer. Percussion channel might be harder to keep high and dry than picking into a flintlock flash hole.
If there rain or that soggy mid to upper 30's snow covered dreary day, it's time to change it out.
I've never had a failure to fire when hunting with blackpowder and I use this method above.
I mainly shoot flintlocks, so other might chime in how to keep the percussion sealed up well. Maybe a rubber automotive brake caliper bleeder cap might be a good try.
If you must leave it outside in the shed, consider storing it with a bag of rice or some dry dessicant in the case.
I store mine inside, it can be done safely, atleast in my opinion.