I've cleaned/lubed many a freewheel, and most all of them "wobbled". Some more, some less. As long as it doesn't cause the bike to spontaneously shift, I wouldn't worry about it.
Although, this week I pulled apart a newer Shimano freewheel that defied reassembly with my tried and true method. Finally figured out the inner bearing race was a different design than those I'm used to.
Most have a simple curved race surface - the inner body can be inserted with plenty of clearance into the cog-carrying outer body. The bearings are held by grease in the outer body race.
This one was so tight, the inner body would not clear the bearings during insertion. That's because the inner body race surface was indented - it had a definite groove that the balls ran in. So, the balls had to be held in that inner body groove to allow the assembly to fit into the outer body. Also, the clearance between the two was much closer. Didn't think of it at the time, but that freewheel didn't wobble. Probably due to that tigher clearance - the outer body and cogs just can't move laterally that much. I surmise Shimano figured out how to reduce wobble and increase index shifting precision by altering design. P.S. - that Shimano freewheel was made in Singapore.