I have used Dino's Tires for spare on my GT. They replaced the tube (they had it in stock), straightened out a dent in the rim and balanced the assembly for a very reasonable price, and even let me watch. Dino's gets a big thumbs up from me.
But, that's just me and one store. Are there any other places that can balance wire wheels? Let me know and I'll spread the word.
The reason this is a burning question is that wheels are either lug centered or hub centered. That determines how the wheel is mounted when you spin it. Almost every tire shop in the world can handle that.
Wire wheels are neither and if the shop tries to balance them without the proper tools they can make things worse.
Here's a link to a Moss Motors Tech Article with details. http://www.mossmotors.com/SiteGraphics/Pages/balance_wire_wheels.html