Howdy Andy, good to see you !!!
My experience with doing this has mostly been with the spiral cut ones, but a few regular, uncut ones too....
Maybe try this:
Have some smoke packets ready & just poke some small holes in them too....not to worry if it's not really continuous, it's flavoring at this point, rather than curing / cooking.....
With the already cooked one, keep in mind it's just basically getting re-heated thru, so no need to cook an extremely long time.......if you have a thermo setup to check the internals fairly deep, go by what your article or the packaging says for finishing (my guess would be 155F)......
ADD the smoke first &glaze toward the end of the time.......that way you'll get the smoke to it & the glaze will retain it's flavor a bit separately..............
IF....it's a whole piece (not the spiral cut) maybe cut in a few diagonal cuts thru the outside to allow your smoke in a bit..............just adding an hour's worth I bet will be pretty rich, as it's already smoke-cured, eh?
The last part I have a question.....are you going to eat when done, or have some & store most (the refrige question) ?
If most or all is to be chilled, then let it sit for a half hour or so, then set in a food grade bag of some type & ice it down.....get it down around 40F, or at least below 60f before going in the fridge....couple reasons:
For the sake of the ham, keep it cold after cooking & for the sake of other items food safety in the fridge, chill it pretty far before storing.............
Have a great Christmas ham (i'm guessing that's what it is !!!)