If he doesn't let you pick him up, here's a trick I use on my ham
Place a small bowl or jar at an angle, and place some food/treats in the bottom. Once they're in, quickly pick up the jar. Whilst they are busy nomming away, you can do a quick examination. If you need to take your little one to the vet, transfer him from said jar/bowl into a carry case suitable for your hamster.
Make sure you tell your vet that the hamster may be unsocialised, so they can handle him without being bitten etc.
Hope this helps! It's great that he's lived so long and so healthily (by the sounds of things) so you must be doing something right and caring for him properly
Also, as long as he seems to be eating fine, running around and on his wheel, gnawing on things etc he should be considered healthy. They are quite robust little critters. He might slow down a bit but it's just him showing his age. Closer inspections can be done using the clear jar method if he doesn't let you pick him up