I have handled enough shooters to feel confident I can do it in many, if not most, circumstances. It has been a very rare circumstance where I wouldn't have been able to bring a knife into play.
Remember you must use strategy and tactics. A good knife fighter would, of course, practice bringing his knife into play. I have only toyed with the idea because I am not interest grappling, but I have grappled practiced grapplers in the past and I am not too concerned with most of them.
A smart person will draw a takedown and have a hidden knife prepared from the beginning. It isn't that hard to draw a takedown now-a-days when nearly everyone fancies themselves a grappler.
Is there a way around it? Of course there is, all techniques have counters. What makes someone successful is their ability to avoid counters when they are executing their chosen techniques.
As I said above......every method has its weakness. All one need do is study the techniques, divine the weaknesses and learn how to exploit them to your advantage!
At the very least you could just let them put you into their favorite armbar and drive your knife into their femoral artery and twist, severe their hamstring, sever their wrist tendons, severe the Achilles tendon, or any other target of opportunity.