In reply to FrJ: Back in the "good old days" I have taken one hand luggage, but given that I also had my Leatherman and a Swis Army knife (legitimatly) in my hand luggage at the time who knows what the rules are these days.
If you contact the airline in advance you will be able to arrange assistance at the airport for those with mobility issues. They might well (as with pushchairs) be fine for you to have your stick in the airport and just take it off you to put in the hold for the duration of the flight, better to arrange this in advance though.