Build a little dry box, very easy to make in a short time with basic materials. I made mine out of ply but you could use anything. Nylon is very (can’t think of the word ) and attracts moisture like a magnet. It really doesn’t take long for it to absorb enough to affect print quality when sat out in open air.
Regarding supports, I rarely use them but they are one of the things S3D is absolutely brilliant for if you can afford it. I’ve not updated cura since 19.something so I’m not sure if they’ve changed at all but they’re always really quite simple to remove when sliced in s3d. You can always try making your air gap larger, some people report success with it but I’ve never managed to make much difference without adversely affecting the finish.