Well, as a member of the post-WWII Stasi, I'd like to point out that English generally has no universally accepted authoritative form of the language to which you can persuasively appeal :)
I agree, it sounds weird. I'd avoid it all together and use on-site.
Edit to add: or, as uncle-comment (?) pointed out with the Wikipedia article, on-premises software is a thing. On-prem might be a good compromise, depending on your penchant for shortening like that.
Sorry for being a grammar nazi, but this one is a serious pet peeve. The singular of "premises" isn't "premise", it's "premises".
https://en.wikipedia.org/wiki/Premises