So, I don’t have an answer, but I think the challenge you’ll face is that the oil you apply nearby will want to penetrate the wood and spread to the area that will be glued.

You could try pre-treating the area where the glue will go with another absorbent coat (maybe even mineral spirits would work) and hope that the oil wont have any purchase to hold onto in that area. Once the mineral spirits evaporate, you’ll be able to apply your glue.

That’s the best guess I’ve got. Best of luck!