Wishing Winston a speedy recovery!
Rather than lift him out of the tank, would it be possible to lower the water as much as the filter allows for it to continue functioning, and have him in that level of water for the next while, but additionally use a plastic tank divider temporarily to keep him in one area when dressing his wound?
A couple of suggestions for keeping the injection frozen are:
Buy a freezer box and keep the injection wrapped with frozen items (eg peas) or bags of frozen ice cubes - not sure how long this would last before you'd have to buy more frozen items to keep the freezing effect.
Buy disposable icepacks (eg Koolpak) but, from experience of using them for injuries, they aren't as cold as bags of frozen ice cubes and only last for short periods of time; however, a combination of them and keeping them in a fridge to maximise and lengthen their cooling effect might help.