If the tire (tyre) has been in use long enough to need replacement or "rotation" it's quite likely that the wheel could benefit from a "trueing." This is done with the tire off, rotating the wheel on its axle and adjusting spoke tensions to remove any wiggles and wobbles in the rim, before re-mounting the tyre.
Since individual spokes frequently stretch after a time in use, this adjustment sometimes results in one or more spokes that protrude through the end of the "nut," presenting the danger of puncturing the tyre or tube from the inside.
There should be a rubber ring on the rim, between the spoke ends and the tube/tyre to protect against this kind of internal abuse, but a spoke end that projects past the protector ring (after adjustment) may need to be trimmed or sometimes individual spokes need to be replaced. The ring itself often degrades to the point where replacement is recommended.
Assuming that you're planning to do the remounting of the tyres yourself, a close inspection of the condition and placement of the protector is recommended - if construction practices in your part of the world are similar to what's most common in mine.
As with auto tyres, tread wear is not the only, or best, indicator of the need for replacement. Most "experts" (including some who don't sell tyres) recommend replacement of auto tyres after about five years (or sooner) regardless of remaining tread, due to "rubber rot" from ozone, uv, and road chemical exposures, and it's unlikely that your ten year old examples retain more than a small fraction of their original "material integrity." Unless prices are significantly different in our respective locales, you're probably due for a pair of newbies.