This is sure an ambitious challenge!
While the weather forecast is on your side, and they say there is only a small amount of snow predicted from the current storm, they could be off the mark. So you won't know for sure how much fresh snow you will encounter.
If you get all the way to Trail Camp, you will be spending a freezing night. An ice axe might be required to get water from the pond at Trail Camp. You might think about camping lower: Outpost Camp. That still puts you in reach of the summit.
In fact, the big unknown is how your body will react to the altitude. (were you ok on Shasta?) You will have effectively no acclimatization (consider getting a Diamox Rx). You might get lucky and be ok, or it might hit you like a truck. Being in great condition makes no difference, in fact, it allows you to get higher faster, which might result in worse AMS.
Ice axe is recommended for the worst spots: Snow is piling up in drifts a few places, so you will be trying to side-slope some steep spots. Review ice axe use: see
this post for links.
Make sure you know where the trail goes. People can really get lost in the snow.
And finally, make sure you don't get in too deep. The mountain will always be there for another trip. Good luck!!