I must be lucky, I've never had a pressure mark on any of my prints from developer tray or tongs, or any fingerprints from handling them either.
I use rubber-tipped tongs for the most part, but will use my hands when I'm shuffling several prints in the developer. I flop the prints into the tray emulsion-side down and then flip to emulsion side up after a while. I agitate by flipping, shuffling and by pressing the print back down into the developer with the tips of the tongs after it has floated up.
Never a pressure mark. I've used lots of different papers, all fiber-base, glossy, from old Kodak and Agfa papers through Seagull and Zone VI Brilliant, Ilford Galerie, Ilfobrom (which I like a lot, really), Slavich, Foma, Bergger, Cachet, Adox MC110 (which I'm really hoping will come back!) etc., etc. I'm now using Foma and Ilford MG.
I'd still like to see a photo of the OP's problem,
Doremus