If the snowshoes are identical and you can strap in your boots to either snowshoes and have your foot line up properly on the snowshoe, then they will work either way provided the buckles or excess straps on the binding don't tangle in your other foot or catch on something. Also check that the pivots swing freely in either handedness. If your feet are naturally splayed or pigeon-toed, then your boots shouldn't be parallel to the snowshoe frame but at your natural walking angle with the snowshoe pointed straight forward.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72