* Why a "designer dog"?
There are many animals that meet their deaths daily in shelters. You might be surprised at finding a wonderful mixed breed that maybe even looks similar (online) to similar mix. I have seen SCW mixes at online adoption sites.
Having said that I have owned TWO purebred SCW rescues. One from out of State as well. When they came to American breeders from Ireland, the lack of care and greedy urgency to make money caused the breed to have a devastating fatal Blood blood disease. This is the fault of US breeders. Sadly, a majority of Wheatens bred now in the US have this in their genes. Not lying. So the pushing of breeding them has hurt the breed and also altered their sweet temperament making them hyper and sometimes aggressive. The standard of a true Wheaten is sweet, not over bouncy and never aggressive. They are also not like other terriers. There are some breeds in non-terrier groups that do possess similar temperaments though. And even looks.
It would be truly devastating to see this breed crossed now just to get a designer dog when the breed suffers. THIS is why you never see them get Best In Show also in major Shows. They are being protected as much as possible while they try to repair the damage. Many don't care though and the dogs die. I have only met ONE breeder in the whole State that I live in that can guarantee "health" from the disease.
I currently have a BichonX. DNA is Bichon, Poodle, Schippekie, Clumber, Duck tolling Retriever. Looks like a small Wheatie. Ha! They are not always sweet and they can be biters. Not always but they can be. My other is a GSX (Blue Heeler, Great Pyre) rescue.
What I sense is that you are attracted to a medium to smallish size blond/wheaten shaggy type pup.
I hope you will look online at shelter and rescue adoption sites and bide your time. He/she will come. Put in Wheaten and some mixes should come up. Also Bichon and other mixes should come up. You might also open yourself to sheepdogX, WestieX, HavaneseX. The temperaments might just surprise you.
I have had around 12 dogs in my life. All have been loved as if my own blood.