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That is quite a normal problem and is often discussed.
A quick once over with milady's nail buffer will work to remove the sharp edge.
~Richard

It is hard to remember to come to a full stop at the end of a stroke on the strop but it is very important.
Strop more slowly and maybe do a count until your muscle memory is trained properly to...

You have good tools, go easy and enjoy them. Stropping is a slow thing to learn and softly softly catchy monkey!
~Richard