E H, if you are looking at re-homing from a shelter & they don't have anything suitable right now I'd say give it a while.. let them know what sort of dog your family could adopt & I'm sure they'll make contact if the suitable type comes in, or if they know of something in another shelter. I had a look at the Limerick Animal Welfare sanctuary there, they didn't have many dogs listed today, but I've been on their site before when they've had mix-breed puppies, terrier-cross types, etc.. quite a few that were non/minimal-shed varieties.
Lurchers are lovely dogs but they do shed like bedamned.. I'm trying to remember what our greyhound & wippet houseguests were like for shedding.. I know they weren't as bad as a labrador, but I think they also shed a bit... Again they're usually lovely tempraments, as are the lunatics of the dog world - irish red setters, utterly bonkers dogs & will run forever. We had a setter, then a lab-cross, but we regularly had house-guests with dogs when I was growing up so I've seen my share of breeds up close. the cocker spaniel got chucked around by our setter, the greyhound was best buddies with him they'd disappear onto lahinch golf course if we brought them onto the beach together. The whippets used to wind up in our beds... And an english setter was practically identical in behaviour to our irish setter.