You might taje s look at some of Ventahood’s ”Under Cabinet” mount pro hood selection. . They offer a lot of options including a broad selection of CFM choices.

Is this for a kitchen that will be used or primarily for looks?

If the former then start with figuring out what functionality you need and then narrow down aesthetic choices from there. Some info here: https://bamasotan.us/range-exhaust-hood-faq/

IMO 500CFM is not adequate for much in the way of venting. The question is how many CFM for the range or cooktop you are planning. Then you choose the style .I love my Vent-a-hood and I had one in my last house too but both 1200CFM

Thanks everyone. Agreed we'd like to go 600 plus cfm if possible. I also love vent a hood but none of their high powered cfm options appear to direct vent horizontally (would love to be proven wrong here but I think their K series is the only direct rear vent and those top out at 250 cfm). If there 9 inch series was direct rear vent I would be all over that. 

 This hood will compliment a new 30 inch wolf range. We have make up air all set up from previous range, however we're hamstrung by the existing ducting a bit being horizontal vent due to previous over the range microwave. 

Thanks again for the help!

Most horizontal venting is accomplished via up and then back, via duct elbows. Post a picture illustrating your situation and why you are asking for something so short.

Here is what we're working with. I suppose could go to some of the 10 inch models but would that sit too low?

There are all manner of pro style hoods with a stainless chimney that can be used there if you just remove that upper cabinet. The ductwork can go up and back. Or straight up. This is not as complicated as you are thinking.

If a solution is derived from having a remote blower configuration, such as on the outside wall of the house, then the number of hoods that can be holed at the back will increase. Keep in mind what you are asking for, however. One can't have a 10-inch high hood shell and put a 10-inch duct behind it. So high CFM will not be consistent with low height and rear ducting.

Since I have a Wolf catalog on hand, I looked into this. They have a 10-inch high under-cabinet wall hood. And the following is an extract from page 154 of the 2023 Wolf Design Guide.

Pro Hoods accommodate a 10" (254) round duct. Low-profile wall hoods allow for an adjustable discharge. All other Pro Hoods have a vertical discharge. For the 24" and 27" deep wall hoods, a horizontal discharge kit is available through an authorized Wolf dealer.

I wouldn't call this message completely unambiguous, so call Wolf for more information. They answer their phones.