Perhaps this is a regional term for axle boots.
I can sort of see where someone could refer to axle boots as axle “cuffs”.
If the problem is, indeed, damaged axle boots, this means that road grit and water are now getting into the Constant Velocity (CV) Joints, and that is not a good thing. The CV joints can take a certain amount of this abuse, but after a few months (and you have no way of knowing how long the axle boots have been compromised), the CV joints will be damaged to the point of needing replacement. In fact, the CV joints on a 10 year old car may be ready for replacement in any event.
Can you ignore this for 1-2 years?
While nobody can predict exactly when one of both of those CV joints will snap, if it happens while you are on the highway, passing a bunch of 18-wheelers, you will be unable to transmit power from the engine to the drive wheels, so you will be forced to coast to the shoulder. In case you haven’t contemplated that type of situation, it can be fatal.
If a CV joint snaps while you are crossing a busy highway or a RR crossing, it also has the potential to be fatal. For some reason that I can’t fathom, most folks seem to envision catastrophic breakdowns as something that will take place in their own driveway or some other convenient location, and at a convenient time.
Unfortunately, the odds are that this breakdown will take place while you are driving, and that could be at an inconvenient time, or in an inconvenient location, or even a dangerous neighborhood. When the CV joint(s) snap, you will be stranded and need towing, at the very least, and as described above, the possible scenarios can be serious, depending on the location.
My suggestion is to take the car to a different mechanic–preferably an indy shop, rather than a chain operation like Midas, Meineke, Monro, Sears, Pep Boys, AAMCO, etc. Ask them to take a look at your axle boots and to show you any damage if they find any.
If the axle boots are in need of replacement, be aware that you can replace the entire axle–including the CV joint and boot–for not much more money than it would cost to replace just the boots. If you replace just the boots at this point, it is still possible that you could have CV joint failure in the future, as a result of the grit that penetrated the damaged boots, so replacement of everything could actually cost less in the long run.