Try command strips. They pretty much work just like velcro and hold up very well.
Depending on how heavy your artwork is you can use velcro sticky tape. I've used it to adhere fabric panels to cabinet doors. You could use it the same way with lightweight artwork, but I don't think it would support a wood frame. I would recommend command hooks for that. They shouldn't damage the walls or paint in any way and they'll stick to dry wall, glass and tile and there are different styles each made for specific weights.
If you choose to go the velcro route, this is how I've used it. https://www.exquisitelyunremarkable.com/2015/03/creating-charm-with-fabric.html
Hope that helps!
Ron have you tried the 3M hanging kits? I use these every Christmas....and when I take the decorations down.....some were heavy.....they didn’t leave a mark so you wouldn’t have to redo your wall when you nail or screw the Velcro on.
3M command hooks. Velcro won't hold the weight.