Would it be wrong if I brought a tray cat to the humane society that cuts my dogs quicks?

A cat started hanging out in my garage, and I started feeding it. When the vets open I'm going to take the cat to get scanned for a microchip. If it doesn't have one then I was gonna give it to the humane society. It has really good reviews. Like 4.7 stars with 200 reviews. The thing is that I used to take my dog there to get his claws trimmed for $5, and every time they would end up cutting one of his quicks. I understand it happens sometimes but it happend everytime. I'm afraid that of they are that careless cutting claws, then they'd be careless with the cat. What do you think?

Would it be wrong if I brought a tray cat to the humane society that cuts my dogs quicks?
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