Would the Apple flavour stay as the vodka dried?
Use corn syrup or piping gel (whichever you already have) instead of vodka for painting a shiny finish that will stay shiny. Paint it on in thin layers and paint twice if you have to.
Using alcohol like vodka (including your apple vodka) is best for painting decorations that do not have to be shiny, because the alcohol evaporates pretty fast.
This is a recipe for a glaze like that used on fruit pies. It might do at a pinch (I would discard any after you are done with this cake). It won't have the shine you really want.
If you have time--check the cake section of your local grocery or craft store, there may be small tubes of piping gel. You would need a few of those, open them up and colour as required, and paint away.
It's worthwhile to order a small container of piping gel the next time you are purchasing supplies by mail order. It has preservatives and will keep for 2 years in the fridge.