Just a reminder, if a passenger requires a seatbelt extension, according to FAA rules, they are not allowed to sit in the exit row. Just trying to read between the lines of your statement saying that "They have a hard time fitting into fixed armrest seats" and that you are looking to sit in the exit row. If it's for other reason, remember that they must be able to perform their duties in an exit row. If neither are the case, then ignore me!

Just a friendly reminder

But to answer your question, IME, yes, the armrests move. As long as the tray table is in the seat back in front of you, they should move.