Late to the party, but just wanted to remind our OP that a Rollator may be a great option for them - they are easy to fold up, (and don't take a lot of space folded) lightweight, offer a place to sit when needed, and something to hang on to while walking. Plus, that handy little basket under the seat - can't forget that!
Just like a wheelchair, it will fly for free as medical equipment, and can be gate checked at the aircraft door.
They start at about $60, and are found at Walgreens, CVS, and of course
Amazon