Until someone with more time can provide you with whatever code is necessary to have it added to the Gmod gui automatically, there is a console command called "setmodel" you may wish to look for more on Google.
I forget it's exact use, and my 20 second search of Google which led me to the source dev wiki led it's link to a 'no wiki content, please create' page.
I remember using the command years ago for some extra models we had on the Ulysses gmod server, and after using setmodel, we had to respawn.
I don't remember if it allowed non-admins or non-svcheat server clients to use the command.
While looking for code examples, I did see some indications that models that were intended as ragdolls will most likely not work as players.
That, and some older player models meant for older gmod versions may not work in the new Gmod.
Seems Garry enhanced player models specifically, leaving NPC/ragdoll models compatible with TF2.
Your mileage may vary, but make sure the original models you downloaded were indeed meant to be used as playermodels, and not just some model to be used in a scene.