What you're looking for can be accomplished in a normal Google Ads campaign
You'd want to run Expanded Text Ads with Call Extensions and Location Extensions.
Then you'd just create super specific Geo targeting. As a result you'd get something like this that only appears in the specific areas you target.
The ad would not show in the maps.
Out of curiosity, lets see if we can create a Local Ads Campaign without a location.
You'd have to not have a location tied to your Google My Business (but rather a service area) and then configure a Local Ad campaign in Google Ads. Though, this would sort of defeat the purpose, as showing in the map is a primary reason people run these.
We can try it out with my account, I have my GMB service area set as all of the US, UK, and Canada (lol) - site's only a year old and I don't want to get put in a relevancy box.
Then de-select driving directions - Store visits will be greyed out because without a physical location Google Ads will automatically make it not eligible.
Then create your ads and proceed like normal. I have no idea how this would actually work out in practice but I was able to make it all the way through the campaign setup.
I'm guessing that without a location set, your map result (see the tabs in the screenshot) would either just not show, or show in the maps sidebar but not have a pin.