Rear derailleur replacement advice.

Hello all,

My rear Shimano derailleur recently broke on my old racer. I want to replace it but it's too old to get the same model and I can't seem to find an equivalent.

Ive measured the old one and it looks to be a short cage which makes sense with my gear ratio. However it has 9 speeds and all the 9 speed shimanos I can find are all medium cages.

Basically does this matter can I still use a medium cage?

Thanks so much for your help!