I don't know if you can make a perfusion pump fit into a shoebox, especially not without very good funding. I do remember a case where a standby team (With a slightly-more-than-briefcase-sized perfusion pump, I think it was this) was working on one of those resusci-anne dolls and they mishandled the pump, causing a whole mess:

I will add one thing that the reporter didn‟t because he had left the room to photograph some of the other CUK members before he lost his light to the setting sun. And that is that the venous blood reservoir bag in the circuit of the ATP exploded due to a misplaced clamp. The reporter apparently missed the timid request made to the meeting‟s hostess, Sylvia Sinclair, for a mop and towels to clean up the water that was all over the kitchen. While it is true that cryonicists often have no choice but to undertake to provide and deliver care for themselves, it is equally true that they should not attempt to do so in ways that make the situation worse for the patient than had they taken a simpler approach that was, in fact, within their ability to master. I had spent most of that day at the meeting trying to convince the CUK group that rather than the ATP, what they really needed was to use a simple, inherently „safe‟ open circuit system open circuit system equipped with a microbubble detector and auto-line clamp, to start cryoprotective perfusion as soon as was logistically feasible and to follow that with cooling of the patient to dry ice. Source (Emphasis mine).

If it were feasible (To make an automatic shoebox-sized HLM or general perfusion pump), it would be worked on, because then you don't have to pay all those expensive hemodialysis technicians (Trivia: Mike Darwin is one) and cardio perfusionists, who remain the only people capable of operating such machines in a manner that is safe for the patient.