Normal scythes (right) can be used by both right and left-handed people. Historically, left scythes were never used as people wouldn't be able to mow together in a group.
The scything movement is very symmetrical and it should not be a problem for left-handed person to mow with normal scythe.
For absolute movement symmetry, and ergonomy you may want to switch between left and right scythe setups.