The first and most important thing to consider is "what does the beer taste like?" The judge doesn't see the recipe.
Just because the beer touches wood does not necessarily make "wood aged" the best fit category for that particular beer. In any of the speciality category the special ingredient / feature needs to be front and center.
That said, based on the recipe I'd agree with the earlier poster. Old Ale might make sense. It is a category with a fairly broad range of possible interpretation, and a hint of oak would not be out of place.
Consider this - enter it in two categories.
Steve in St Cloud, MN
Tap 1 - Brown Raccoon Braggot
Tap 2 - Munich Helles
Tap 3 - American Wheat
Tap 4 - Scottish Export
Tap 5 - Strawberry Rhubarb Maed
Tap 6 - Sylvia's Apple Pie Cyser
Bottles - Jolly Pumpkin Bam Biere clone, Long Winters Nap Barley Wine - 2012, 2013 & 2014, Flanders Red,