Yes, I think you nailed it, it makes him feel better. I warm up the wipe or use a soft warm cloth. You bath your dog every 10 days? I have heard that it's not good to wash our havs. frequently. I am lucky that my dog stays clean other than the paws and face washes but I think it would stress him out beyond belief if the groomer came every 2 weeks.
Kodi has had a bath weekly since he was a tiny pup. There is nothing wrong with bathing frequently as long as you use mild shampoo and a good conditioner. We don't wait weeks to bathe ourselves!
If you have a hunting breed that has protective, waterproofing oils in their coat, you need to be careful not to strip those, as they keep the dog warm and dry outdoors in bad weather. That's not an issue with our dogs… they don't have any waterproofing no matter what you do!
And honestly, even among my friends who show their hunting breeds as well as do field work with them, they STILL get bathed about weekly. They are just very careful to use products that don't strip the oils. The dogs look great, and don't smell bad, as many dogs of hunting breeds do!
If you are happy with Django's state of cleanliness, that's fine, but it wouldn't do his coat or skin any harm at all to bathe him more frequently. Dogs who are bathed frequently get used to it, and it's just not a big deal in their lives.