#1, hidden but accessible - is the definition of concealed carry... Just saying, careful. Some cops, some states, EXTRA dick about such things. & Yes, I've had friends get charged with concealed weapon (reads like gun in the penalties) for things like a leather-sap... Or the walking stick... Because cops wanted to be dicks.... So, just be aware.
#2 - reinforcing the sheath AND the pack will help it stay on better. Putting a heavy thing attached to the pack in a spot most aren't designed for carrying weight - it'll cause the pack to tare well before it's time.... So, reinforce the back of the pack too... It'll add stability for your blade and keep the pack in top shape.
#3 - thread options.... There is ofcourse the old standby, Dental Floss.

Just remember, lots and lots of layers. OR, another option - they make fishing line, still thin like thread, but ridiculously tough, for some of the bigger ocean game fish. Sometimes, a good tool, is worth the investment. AND the third option.... They make very thin, yet still strong WIRE.

Sometimes you can get it as picture hanging wire at the hardware stores, other times, you have to go to the craft-your-own jewelry store and get jewelry wire. But either of them should totally have a wire thin enough to double as thread. So that's an option too.