What size pump for my mushroom head?

I'm new here and seriously consider PE. My current size is 6" NBPEL, but only 4" MSEG, however 4.25" HEG, if I wear a cockring and do kegels the head will expand to 4.5", but the shaft remains pretty constant as 4". This gives me quite a noticeable mushroom head.

I am not too bothered about my 6" NBPEL, sure, bigger would be better, but at first at least I want to focus on girth gains as my girth is definitely on the smaller size of the spectrum.

I am in the UK and looking for a gauged pump, but I am wondering what size cylinder to get. I understand you should divide the girth by Pi, and then add add a little for growth.

Given my HEG is bigger than my MSEG which size do you recommend? Any where good to buy from in the UK without expensive shipping costs?

Also I am a newb, so looking for any other recommendations on PE routine to follow

Thanks