i guess I'm not exactly sure what the "wobbles" are but I would check out the headset for excess movement and the wheels for bearing issues or being out of "true". So, in answer to your question, a different set of wheels (trued up and with properly adjusted hubs) may fix the issue.
BTW, I'm glad that I won't be chastised for reviving this very old thread but I AM glad that it's been resuscitated. I have a "frankenbike" that is built around a mid 80s Raleigh TECHNIUM 420. I'm pretty sure that not a single component beyond the frame and fork, is OEM! The guy I bought it from had stripped it down for painting (it didn't really need it but he didn't like the mauve color). Somehow he misplaced the components and/or lost them during an Army PCS move. He had neither the money, time nor know how to bring it back to rideable condition. At the time, it was a "pity buy" to relieve him of the burden. I'll post a pic or two later.
Bottom line, the Raleigh TECHNIUM frame allowed for a nice riding bike in spite of the mishmash of components!