Greg mentioned "those electric uprights that look like a stick with an end pin." You don't see them too often, which means that the second-hand/discount-price market is probably pretty thin, but anyone who intends to continue playing the acoustic bull fiddle as his primary instrument might find that particular type of electric to be a good choice ~ you don't have to learn a whole new posture, attack, technique, etc. They're not really any bigger than guitar-style basses, and look pretty lightweight, so one of them might meet your needs.

Of course, there are many bass players who double on the acoustic upright and the electric bass guitar. Not all of them opt for the fretless models. If I were you, considering that you're interested in this new instrument as a strictly secondary option, I'd be shopping for a used instrument of the most commonly-available type, that is, a fretted Fender (or similar) electric bass.