A little beeswax can be used to snug up a loose ferrule. Rub a hard 100% beeswax candle on the male end and check the fit. This solution will attract dirt so you will want to clean and reapply it often. I carry an old chapstick tube filled with beeswax for just this purpose. This fix has a long tradition in the cane world and can make a surprising difference, a common problem on vintage cane.
I have read of folks 'shrinking' the female ferrule using a lathe and tool made from a pipe cutter. The metal cutting disk is removed from the pipe cutter leaving just the smooth rollers. The lathe is turned at slow speed and the tool tightened against the ferrule to shrink it.
Nickle silver ferrules are manufactured slightly over sized and hand lapped to fit. It is possible an over zealous craftsman took off too much material but unlikely they would damage both tips to the same amount. For this reason I would inspect the butt section with extra attention. Use a good light and magnification. Make sure the 'loose' part isn't in the cane to ferrule connection. Look for hairline cracks in the thread wraps that indicate movement. It's not too hard to re-glue and wrap a ferrule if that is where the problem is.
Also, make sure the ferrules are fully seated. A small obstruction in the female could be keeping both tips from snugging up. Do you actually feel a wobble or just hear/feel a click. Clicks can also be caused by loose guides, esp. the stripper.