Once you have selected a taxidermist compare their dip and pack prices to their finished euro prices. They are usually not much more to just do a euro. However, I have seen where the euro prices are absurdly high and it actually would be cheaper to dip and pack euros and flat skins, and just degrease and whiten the skulls on your own at home.
If you get them dip and pack, they may mistreat the skulls because they figure they will be shoulder mounts. You'd think that this would be clear if you didn't have a bunch of capes with them, but I suspect the guy cleaning the skulls doesn't get all the information and is just doing what they normally do at his station.
The double edged sword is that if you have the euros finished there, some places paint the skulls white, or paint the horns black, or apply a very dark oil based product to darken the horns. So, if you like them more natural looking, it might not come back that way, and you will have to investigate and communicate with the specific taxidermist you use on how their finished skulls come back.
If primate and swine are completely finished taxidermy they are supposed to be able to come back with your other animals and not supposed to need to go to a special facility. However, a lot of it really seems to depend on what agent inspects the crate that day and what they think the rules should be.