[Osem]

Not sure I've understood your problem totally but if I have, how about using something like the plastic tube from one of those trigger spray bottles. I often keep the tubes from those for joining things like my small bore garden irrigation system - not that Ive used it much for the last few 'summers'.

These tubes come in various diameters and if you could find one which slips nicely inside the fridge hoses you should be able to glue it in place using a waterproof superglue. I've done this successfully in the garden using a mains pressure water supply with no leaks.