Shifting without the clutch doesn't hurt the syncros a bit. If you do it right the gears are spinning with no load on them, just like they are when the clutch is depressed.
I definitely don't want to nitpick a technician, but in case there are any inexperienced drivers who start getting ideas about this, "doing it right" means exactly matching the RPM of the counter shaft and the output shaft before you engage the next gear, which I would argue is very difficult to get perfect. Close yes, perfect no. Any difference in RPM needs to be taken up by the synchro for that gear to match up the speed of the output and counter shafts, which means there will be
some wear. Or you mash the synchro sleeve or baulk ring teeth or the gear itself, which is even less desirable than just wearing the synchro.
Sorry to be pedantic.
EDIT: I suppose I should add that you'll also wear the synchros
some even when you use the clutch... how much they wear is just a question of the difference in RPM between the shafts. Still have to get those 2 shaft speeds synchronized.
EDIT 2: true, if you shift either way with great skill, you can make the synchro wear fairly low, and they can last a very long time, but they’re still wear items. Just avoid the bang shifting unless you like rebuilding transmissions