It is unlikely that they will ask you to use the frame, I have never been asked in 5 years or so of flying within Europe with a rollaboard that has in reality been a centimetre or two too big for some of the carriers (EZY included) regulations. Although I have been asked at the gate to put airport shopping purchases in my carryon and lady travelling companions have been asked put purses etc into their main piece of hand luggage before boarding.

Regarding getting a piece of luggage to exactly fit EZY's specifications, I personally have not seen such a piece on sale, although I have seen bags advertised as "meeting BA hand baggage restrictions" in the UK and similar pireces on sale in Germany advertised as LH hand lugage compliant.