Almost certainly you would need a needle on a tubing for this and an assistant - so you could scruff the pup and hold the needle and someone else operating the plunger - if you can use a butterfly needle that might be best - however I think 25G might be the smallest available though and this might be too large for you in P11 pups.
For P0-P2 injections we have used a 32G or 34G Hamilton needle and some Polyethylene tubing and Epoxy resin to make a very similar construct and place it on a larger blunt needle and syringe; however these are not ideal for repeated sterilisation as they are quite fragile. The skin may also be too tough for the small gauge.
No sure if Simon N Waddington has any suggestions about where to access the vessel in this age?