I never wear gloves while doing regular prints and my hands keep dry during the process. Taking the paper from one tray to the next is easy with a tong for smaller formats. But for bigger paper sizes a tong may not be that practical. Therefore and due the small size of my darkroom, when printing that big I do one tray development. So I place the paper into the dry tray and then pour the developer over the paper - that way I also can make sure that all the paper gets covered with developer within seconds. For FB I develop three minutes with constant agitation, then I pour back the developer into the bottle (using a funnel). Then I pour in the stop bath etc. Since I rarely print that big, I do also all the washing, toning and again the washing in that one tray, so the first time my fingers get in touch with any liquid is after the final wash, when I take the paper out of the tray.

That might sound impractical for you, but it works very well for me.