I think you are going to have the best luck by drilling a small hole and sticking a screw through the lid. The only adhesive I would consider for your purposes would be a high temperature resistant epoxy.
I was in the same position as you recently (but with an aluminum pot). I found a 99 cent drawer knob from a hardware store and finished it with Tru-Oil (which is basically a tung oil/linseed oil type finish) for water resistance.
I first tried some super glue and that quickly fell off after only two boils or so.
I decided that screwing the thing on was going to be the best fix, so I went ahead and did that. Here is what my lid looks like now:
There are a few things to consider when screwing a knob onto a pot lid:
1. It's probably worth using a stainless steel screw for job this because it will be MUCH more corrosion resistant in the long run than the cheaper zinc-coated screws. I think this is actually relevant because the screw will be subjected to an environment with lots of heat and moisture.
2. To avoid any potential galvanic corrosion issues between the titanium lid and your non-titanium screw, I would suggest using a small nylon washer to physically separate the screw from the underside of the lid.
I hadn't thought to use a piece of cork like you are proposing to do, but I think that will work just as well as my finished wooden knob. It will certainly be cheaper and less work, and cork is very resistant to rotting even in damp conditions.
Best of luck with your project!