I don't think there's many restrictions on what you can carry. Around aircraft you'd prolly have to have it marked and tethered for FOD reasons,and you'd prolly get some funny looks having that Randall on your belt working the chow hall.
I'm fascinated by this military/knife thing. A similar thread to this was brought up before w/everyone feeling the need for big combat knives. Nowadays,the idea of needing to drag along all kinds of personal gear is becoming outdated. My Dad(Navy 'Nam vet) is constantly amazed at the gear I have,and I'm an AF computer geek. Plus,we don't fight the way our daddys did. With the level of C&C we have today,the chance of having to make it on your own are slim to none. Unless you're aircrew or spec forces,both of whom get top-end kit. You're either going to have support,which makes your own stuff redundant,or you're captured,in which case you don't get to keep your stuff. And as I said before,if something happened to my weapon,I'd look for another one before I pulled a knife. Knife vs assault rifle is not a good idea.
If/when I get deployed again,I'd take an LED headlamp,a multi-tool,and a mid-sized folder. Basically what I carry every day. I'd be more interested in bringing things for creature comfort than survival.