you should be able to squeeze in a 25" Arcade CRT width and height wise but I don't know if you'll have enough depth to fit the neck board without issue.
IIRC the mounting holes on my WG U2000 were about 19"x19" the "visible area" on a 25" tube is 15" high x 20" wide add a little bit around the parameter for the frame and you should still be good in that regard.... heck a 27"/29" might even fit height and width wise.
I never measured the depth of my 25" and the only monitors I have outside of cabinets right now are 27"/29" Tri-Syncs.
I know there were a few obscure arcade monitor models designed for shallow cabinets but you'd probably have a hard time finding them.
you could also consider cutting a hole in the back of your cab to accommodate the neck-board... this isn't unheard of, several legit arcade machines did this.

The other thing you might want to consider is weight... those 25"+ arcade monitors weigh upwards of 60lbs and most of them are mounted on metal brackets with carriage bolts right through the side-wall of the arcade cabinet... depending how you have it built a wooden shelf might not be enough.
If you want I can measure the depth of my 27" tonight just for reference.