I'd strongly suggest waiting until next year so you have the entire summer to lay low, heal, and get through part of the ugly duckling stage.
One of the most critical things I learned from this site before my own FUT surgery (done back in February) was how long it would likely take before I could realistically hide the fact that I had surgery. It wasn't until about 3 months post-op that I felt I could start to hide it. Before that, I wouldn't be caught dead outside the house without a hat. Like you, I strongly prefer that no one (other than my fiance) know that I had surgery. It would have been an absolute DISASTER (personally) if I had relied on the websites or clinics that said I could go back to work 14 days post-op, and if I had planned to do so.
Thankfully, I followed this site for a while and reviewed countless people's experiences and pictures before I made the decision to have an FUT, and 3 months is roughly the timeline I was anticipating after looking through so many other people's journeys. Of course, I realize everyone heals differently. But honestly, if it wasn't for working from home for an extended period due to COVID, I don't know how I could have hidden my procedure.
With all that said, my FUT procedure did involve shaving both the recipient and donor areas (which is the norm), and I've only reviewed a handful of "non-shave" cases on this website. Therefore, I can't speak to what the timeline might look like for when you could hide a non-shave procedure, but I imagine it would be much earlier.