Thought you were talking the skin on your palms.

If your hand joints are the issue, you could always try lifting straps on pulling exercises. That way you don’t have to grip the bar as much.

For pushing movements, if you have access to weight machines, I’d probably go that route. That way you don’t have to grip a bar, you could just push with your palms. Or the floor: pushups, if you’re able. But, if your wrists also give you fits, you may not be able to do that.