There are a couple of things to think about.
1) As a Vet handler, ALL your dogs MUST jump 4 inches lower. If you only have one dog, not an issue. But if you get a second dog, it might be young but it must jump 4 inches lower if you enter as a Vet Handler. Just something to think about.
2) Both skilled and VH give the dog an 8" height break and also more time (SCT) for each height break. So the dog would get more time to finish a course when running as a Skilled Vet Handler than just a Skilled category height break, or just a VH division height break. Something to think about if time is a problem for your dog.
3) The SCT is based on the jump height the dog is entered in.There is no difference for the SCT on whether you enter Skilled or enter as a VH. It doesn't matter HOW the dog got in that jump height....be it as a Proficient height, Skilled height or as a Vet Handler or Vet Dog division.
For me, I run two dogs....one is almost 7 and short strided, so jumping is more difficult for him. I am a Vet handler, so that dog runs skilled vet handler and he gets an 8" jump height break. My second dog is young and doesn't need the 8" break, so he is entered as a Proficient Vet Handler and only gets the 4" break (for VH). If you don't want your dogs to get a lower jump height at all, then don't enter as a Vet Handler and simply enter your dogs in Proficient.