Yes, you are correct. It's already cooked and you are just reheating it and adding some extra smoke flavor.
I would not use too strong a flavored wood on a pre-cooked ham like that, as they usually have some smoke flavor already. I usually go with apple and spritz the ham with apple juice mixed with Jack Daniels mixed 2:1 with juice being the "2" (sometimes I use pineapple juice mixed with Jack, but I need to filter it as there are small fines in pineapple juice that tend to clog my spray bottle head). I usually spray at the start and again about every half hour until I apply the glaze (if any).
I smoke mine at 225* until they reach an internal temp of 120 to 125* (remember it's already cooked). If you want to put a glaze on, I do it after the ham hits 110* and you can make your own or use the pouch that comes with most spiral sliced hams. Straight from the fridge to done takes around 4 hours (go by temp, not time) and you can speed it up with higher temps but I prefer 225*. Prep is basically taking the ham out of the fridge and opening the package. No rub needed, just toss it in the smoker and smell the thin blue smoke. You can use a rub if you want (I don't), but just be aware the sugar in rubs can tend to burn if you end up smoking at higher temps so keep it low and slow if you go with a rub.
They are super easy, fairly quick and painless to do. I highly recommend it. Here is one I did in WSM for Thanksgiving