I took a quick look at the diameters of the 50 series and 60 series tires along with revolutions/mile at Tire Rack for a Firestone tire as an example:
235/50-17
Diameter = 26.3"
Revs/Mile = 792
235/60-17
Diameter = 28.1"
Revs/Mile = 741
So, the taller tire profile tube might be a bit crowded inside the 50 series tire. That could lead to the type of folding or unhappy creasing of the tube upon installation. It would be better to find the proper tube, but your installer can coach you on that. A suggestion would be to spray the exterior of the tube and the interior of the tire with silicone spray. Then add a bit of air to the tube and move it around until you're pretty sure there are no folds or wrinkles in it. It's also important to get the fill valve accurately aligned with the wheel's hole without stress on the tube.
This is an interesting problem in today's "tubeless" world! Proceed with Caution!
Best wishes,
Tom
PS: Post a pic of your Bird with the Wire Wheels when you get a chance! Thanks!