I'm trying to visualise what's moving. Is the freehub body moving even though the axle is not, or is does the whole wheel wobble when the axle is held tight. If it's the first, then then the problem is in the freehub itself. You can service the bearings, but if there's another problem, you're probably sol. From
Park tools:
Be aware that it is not recommend to completely dismantling the freehub itself. There are no parts available, such as the pawls or springs. The small ball bearings are available as replacement parts. However, if the bearings are worn out and require replacing, it is very likely the entire freehub is needing replacement. The blow-up image seen below is a ball bearing type freehub.
If the whole wheel has play, then obviously just take it apart and service the bearings. I'm hardly the most experienced mechanic, but the amount of time this takes drops very quickly with a bit of practice, as does the frustration level.