new current account during mortgage application without overdraft?

I know that the general rule is not to do anything to change your credit reports during the re-mortgage process. We have a low LTV and no missed/late payments ever.

I want to change both of our main current accounts due to imminent changes to both of them - if you apply for a new current account but with no overdraft facility would they still do a credit search? I suspect the answer is yes.

I realise we should probably just wait but would prefer not to.

Thanks