How to randomly choose a hex tile
The best way to deal with variable count randomization is to use a drawing bag

Create two sets of tiles.  Whenever you add a tile to the board, add its copy to a drawing bag. 

Now whenever you need a random tile, draw it from the bag.

This technique requires all your tiles to be unique. If they are not unique, and can't be given a unique identifier, then create a double set of numbered tokens, and assign a number to each tile as it is placed. 

Deck vs Draw Bag

StartPlayer mentioned using a deck, which is also an excellent suggestion. The two options have slightly different use cases, so which one you choose should depend on how you need them. 

Draw bags are better if you are frequently adding items between draws, because it is easier to shuffle a bag, especially if there are only a few items.

On the other hand, a deck is better if you need to remove specific items in a manner besides randomly drawing them, because it is easier to search a deck than a bag.