Ah, I thought it might be but erred on the side of caution.
I won't bother trying a different adapter, as I only want to be able to say to the retailer I've tried it, & I know my own adapter isn't faulty as such. Thanks for the offer anyway. I will probably just keep it as a USB mouse, but report in the error for their future reference (and other customers) & see what they say.
(& report back )
edit for the record; basically, 'thank you for informing us of the issues with the mouse. This information has been passed to the relevant team to be investigated. Any necessary changes will then be made.
Thank you for taking the time to write to us regarding this matter.'
(I did say I would not be returning the item as it was not really worth it for a mouse that is usable to me albeit not as ordered - but still, 'Sorry we sent you the wrong item' would have been nice).