I have recently had a couple of deliveries of shrimp using the Royal Mail next day by 1PM and that went well. I have had may deliveries of shrimp using that service over the years and never had a problem and to be honest, when I look to buy on ebay I will only buy from someone using that service (but that is due to this place isn't the usuall 'numbered house in a normal road' address and most courier drivers aren't all that bright so it confuses them, but that is specific to where I live and ANY ordinary address should be ok). There are a number of overnight couriers like DX and APC who I think would deliver fish but you will need to do your own research as to whether they have a licence for carrying fish and/or whether they will even deliver fish/shrimps, they keep changing since COVID, some that did now don't, and some that didn't now do, and it keeps changing???? Even Royal mail isn't what it was, as now they tend to just leave/abandon the package somewhere, rather than getting a signature and handing it to someone in person, and I think the delivery time may now be by 4pm, whereas it was by 1pm? I have only ever had one fish delivery through an overnight courier (not sure who it was but it was before covid, may have been DPD?) and that went ok as well. Any 24 hour/next day delivery should be fine but I would use one that will deliver live creatures specifically, and mark the package as such (and put the buyers phone number also on the outer package) as obviously a bit more care should be taken with live creatures.
There are a lot of ebay sellers over here sending shrimp through the post, the parcels I get usually are marked 'live creatures' and I doubt most (if not all) aren't registered/licenced, or pet shops etc so I can't imagine there are any real restrictions or requirements. I imagine shrimp and fish are classified the same????
Packaging is pretty straightforward and you have mentioned all the aspects in your post, double breather bagged, packed in a polystyrene box padded with newspaper (and heatpack if needed).