I was former SF - served in Nam in 68&69 on an A team in the Delta. As far as a knife goes, you're going to be chopping branches and making firewood / kindling and maybe cutting some rope. You're not going to have a lot of time to do much of anything as they are going to constantly play with your mind, keeping you tired, frustrated, giving you problems that don't have solutions and oh yeah, did I mention playing with your mind? Besides cutting some wood, on one of my FTX's during training / selection, we stole a farmers goat, slit it's throat, bled it out, butchered it and had it for dinner. That, and some snapper turtle one of the guys caught too. Take along something you don't mind losing, something sharp (you can always sharpen it on a local rock if you need to) and something that will hold up to very rough abuse. The choice is yours, but for me it would be a fixed blade. We had K-bars issued back then, and some of the guys had Gerber Mark II's, but they were mostly for show as they were useless for a training exercise. In Nam it was different, they served their purpose well, but you're not going to be dispatching any sentrys (at lease not really eliminating them in training). A fixed blade, something to pound on to split wood etc.. Trust me when I say it will be the last thing you're going to need to worry about. As I said, no sleep, critical decisions, problems with no workable solutions - it's all about attitude. Teamwork is what counts. Attitude is what counts. Stamina is what counts. Leave no one behind, offer encouragement, follow directions and improvise. Never quit.
I wish you the best of luck. Should you make it to being awarded the beret, know that the men who have gone before you were the best, and that you need to strive, every day, to earn your right to wearing the Green Beret. It's a small, tough community of men, who in some cases have given their lives to protect their comrades (several of my close friends are on the Wall in Washington). It's all about teamwork my friend, being an individual with an ego is the fastest way to get you eliminated from the course.
Good luck, stay well and let us know how you do when it's all over.
I wish you the very best.