That's what I would do . Shouldn't be too hard to find an adhesive. What other option do you have ?

A polyurethane construction adhesive such as the link below. You can get it at most big box or hardware/lumber yards as well as paint suppliers. You would want to cut some strips of wood to act as a clamp by bracing off of the opposing wall. It doesn't need to be anything heavy duty,(like a 2x4), something bendable and strong enough to keep pressure on the base board until the adhesive sets. You could even use scrap pieces of base if they are long enough to go from a point across from the glued base. Cut it slightly larger than the span and bow it in tight.

Here is a link that might be useful: pl adhesives

A bead of construction adhesive like Liquid Nails would work.

Be sure all sides of the wood have been finished before gluing it on.

The last thing you need is pint blowing off when water gets under the baseboard and soaks into the wood.