Normal atmospheric humidity shouldn't have any noticeable effect on the powder in a paper cartridge, no more than it would be an issue with powder stored in a flask. The paper itself shouldn't be affected either. I have shot paper cartridges that I made up years ago without issue. Some of my revolvers have cases with flasks and I usually keep those flasks filled and use them when I take those guns out shooting .......... no issues. Actually getting wet would ruin a paper cartridge but I wouldn't worry about the humidity having any more effect than it does when using loose powder. Some original paper cartridges were treated (shellac, lacquer, etc.) to make them sealed against moisture but it was intended to protect against them actually getting wet in service. For the modern day, hobbyist shooter it shouldn't be an issue unless poorly stored in an extremely high humidity environment. I have lived in some areas noted for high humidity for a good part of my life and it just hasn't been an issue.
FOR SALE .50 Cal T/C Renegade, Excellent Condition!
