The oil cooler plate is nothing more than a piece of thin aluminum with 4 holes in each corner to match the holes around the oil cooler. I've got the same engine and can provide a bit of insight (anything else requires an A&P). BTW officially this part is 67769-04 on Fig 58-15, page 3B11 of the Piper Parts Manual and is named the Winterization Kit Assembly, which is nothing more than a placard and the piece of Al. I remember seeing a photo somewhere online but can't find it now.
Find someone on your field with the same engine and ask them to show you around the interior where the oil cooler is located (if you don't already know the insides)
If they have one of the plates, take the measurements otherwise....
Take off the top cowl.
Stand on the pax side of the engine and look on the top left, just below the baffling, inside the engine area. You should see a hole about 3 in across - that's the intake for the oil cooler. Around that big hole are 4 tiny holes, in each corner.
Get a piece of paper, tape it to the hole, then mark the little holes. That's where the screws will go.
Note: Some people use duct tape or Al tape across but there's a chance that the tape may some off and get ingested and block the oil cooler.
Find the local EAA members around your airport and ask them (bring something either liquid or really good munchies) to cut a square piece of scrap Al and punch the holes for you.
Find the appropriate washers, bolts and locknuts to fit (I've seen U clips used very successfully).
And there you go. I only attach the top 2 screws on the plate.
Now you also need a placard (which should still be in the cockpit on the panel) that states the Winterization Kit should be removed when the outside temp is above 50F.
As owner/operator you can install/remove the Al anytime you want. Officially, you should also make note in the log book.
Lastly, find an A&P and have them bless the new part that you have just fabricated to AC-43.13B Acceptable Methods, Techniques and Practices, and away you go.
As you watch the oil temp you may find that covering the entire oil cooler hole is raising the temp too much. Take a pair of tin snips and cut a bit off the bottom of the plate.