I went to the DW in North Shields, they had shorts there, but I cleaned them out of socks. I got them to call the DW in Byker, who said they have socks but I didn't ask about shorts.
The shorts don't seem to be in nearly as short a supply, so if I were you I'd try Byker. I would've got another pair of socks for you if they had any more in North Shields. There may well be one of these rajis who doesn't want socks too small, I dunno.