The only thing a synchromesh cone does is to speed up or slow down the input side of the transmission to match the output side. If you don't have those cones (or something like them), then it is up to the driver to do it. Usually it is easiest by using the clutch & throttle.
I still maintain that if your shifts are smooth & silent, you aren't hurting anything - regardless of clutch use.
It is possible to damage the transmission during shifting even if you are using the clutch.
It is quite easy to KNOW if you are causing damage - grinding noises, shifter vibrating as it goes in gear, lurching, etc are all indicators of damage occurring.
My vote is to use what ever method that works for you to enable the smoothest shifts possible.
Smart people with limited funds will, of course, start with the most common method - & that will involve double clutching. . .
BTW, as I understand it, the double clutching event is:
Clutch in - unloads drive train to allow you to slide it out of gear without any load on the gears.
Clutch out - allows you to use the engine to speed up or slow down the speed of the input gear to match the speed of the output gear. (takes the place of the synchromesh cones)
Clutch in - allows you to slide into the desired gear without any load on the gears.
clutch out - allows the engine to supply power to the rear wheels.
Bottom line is the gears have to be at the same speed to engage - it is up to the driver to get them there . . . .Unless you have some form of an autoshift.