I've only used the soapy water method. It has worked well. There are some good how-to videos on youtube.

I do recommend sanding down to wood, primer, and paint before putting on new decals. This will give you the best surface to apply your decals to.

Very important to use a primer first.

I'm not sure what the finish is on Demo Man but use an oil based enamel like Rust-o-leum.

I think at least a week to let the paint cure makes sense. I wouldn't do it any sooner than that.