Artos,

First off, my hat off to you for serving in our armed forces, thank you for your service.

Take the Mountaineering class, you have nothing to lose and all to gain, especially if you're not all that familiar with snow travel on a mountain.

I would say you will likely need crampons or microspikes at least in mid-late May. The switchbacks will more than likely be packed snow or ice then even if not much snow is around elsewhere to contend with. Most of the switchbacks are not that steep, but a slip and fall here could ruin your day or worse. A axe would also likely be a good idea, especially if you opt to ascend via the "chute", the slope to the west of the switchbacks. But...if you are climbing in conditions that warrant their use, you are best served to become familiar with them for your own safety.

As far as what conditions will be like in three+ weeks, it's anyone's guess if a late season storm will dump some more snow, but it appears to be shaping up to be a lighter snow year in the Sierras, others can comment in more detail on that.

Where are you coming from? If you live at sea level, you should become familiar with how your body reacts at higher altitudes. While the main trail is "easy class 1" it spends a lot of time above 12,000ft.

Last year, I climbed Whitney on the Main Trail on May 12: below is a trip report with some photos to give you an idea of conditions then.

http://www.14ers.com/php14ers/tripreport.php?trip=11767&parmuser=nyker&cpgm=tripuser

For a shot of what the switchbacks looks like in lighter snow, see the photos below from my trip in November.

http://www.14ers.com/php14ers/tripreport.php?trip=13143&parmuser=nyker&cpgm=tripuser

Good luck!