What if selecting the decks to use for the Random feature could be done on the fly just before selecting Random? If the deck list had a way to select multiple choices, be it by clicking once to highlight it or filling a check-box, and then a Confirm button, it could choose one of the two, three, four, etc. and leave it the only one still selected. Selecting only one and hitting Confirm would, naturally, just select that one deck for use. It would add an extra click when selecting just one card and would require coding beyond having a drop list, but it wouldn't require setting deck attributes ahead of time.
To avoid having the single-selection become a two-click process, it could alternately be created such that selecting Random enables the extra highlighting or check-boxes while just clicking a deck name first would function as it does currently. Or, perhaps easier yet to code, leave the deck drop list intact and pull Random out of it to its own alternate choice as described.