First off, don't do it alone. no matter what. Thats just mountain safety 101
You can for sure ascend the chute as a first timer. Walking on crampons doesn't take any special skill. Just a little patience. Don't rush your steps. Plan every move out 1 by 1. The axe makes a nice grab handle when planted well. The chute is not technical climbing. Its just a wee bit steeper than you're probably used to. There is currently no other way up the main trail, so if you're sketched out, don't waste your time. Go later in to summer when you can do the switchbacks. If your not going to glissade down, but rather walk, then know how to self arrest with the axe. Theres tons of videos on here on how to do it.
The only solid advice I can really give is, I had 5 people in my party that had never ever worn or used crampons or ice axes. We glissaded down with no incident and traveled safely back to our cars in one day. It just takes some patience, common sense and understanding to use that equipment. Yes I had done it before so I was able to coach. So maybe try and link up with somebody while your up there and travel in a safe group.