Cart before the horse...

Did the toilet rock with the original wax gasket? If it didn't, DO NOT cut the flange down, buy yourself another wax gasket and do the job properly. The waxless ones will degrade much faster than the wax will and require a much larger space between the flange and the base of the toilet to fit.

If you do replace the flange with the plastic "screw-in" style, you must anchor the flange to the floor. Since you're on concrete, you will need a hammer drill and expansion fasteners to do it. The toilet bolts to the flange, without anchoring the flange to the floor (or the pipe for cast iron), the toilet will rock and can pull off the floor/pipe.

The toilet must be rock-free if you want the wax ring to last. Consider using caulking around the base. A lot of plumbers frown on this, but I'm pretty sure it's because they like callbacks.

Another tip: SKIP the wax rings with the plastic funnel built in. They rarely (if ever) stay aligned when the toilet is pressed down and can cause water to splash out or cause nuisance clogs due to the misalignment with the drain horn on the toilet trap.

A rock-free toilet with a properly-installed wax ring will be trouble-free for decades.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]