Don’t think you’ll get much smaller than that, unless you can find something/rings to do an old 3/4” tube. Anything with a 1” tube is gonna obviously be about a 1/4” bigger than (1”), in order for the ocular to thread on to a 1” tube..

Looks like an old Weaver K2.5 is about 1.25”...

https://www.vintagegunscopes.com/1inchscopes/weaver-k25-brass-excellent-c1947-48

Later models may vary slightly..

This might give you some specs on some 3/4” and 7/8” tube scopes-

https://www.vintagegunscopes.com/fixedpower3-4and7-8