What would be the best way to glue two surfaces which have already been finished with Danish oil and then wipe-on poly?

One surface would be the cut edge of ply, the other surface would be solid wood. Specifically: a long 2 1/4” width of solid wood capping two other edges of ply separated by a 3/4” gap.

I won't be able to biscuit or dowel, but the good news is that this isn't structural - just a finished surface. Nevertheless, it's not an ideal situation, so some collective wisdom would be helpful here.