Not sure what reasons you would rather not go to Mitsuwa, but I have one specific suggestion, and one not so specific.
Specific. Same area as Mitsuwa.
(With the temps in summer, no matter where I go for sashimi, I'd bring a small cooler with ice packs)
About 1/2 mile south of Mitsuwa, there's a strip mall on the E side of Arlington Heights Road, there is a Japanese market in there. Smaller than Mitsuwa. Less "Hustle and Bustle," but also a smaller selection of sashimi grade fish
Tensuke Market
3 S. Arlington Height Rd
Elk Grove Village, IL 60007
(847) 806-1200
Not so specific:
I once heard that many of the sushi joints get their fish from the places on Lawrence around the 3000 west-ish area. I never got any names of actual retailers, but I did check out a few of them, and found nothing that trumped the freshness of Mitsuwa or Tensuke. As for your two places, I have not even been to the Supreme Lob store in Lombard, although I pass it frequently enough, and I have never bought sushi grade stuff from The Fish Guy.
We cannot be friends if you do not know the difference between Mayo and Miracle Whip.