My calipers say the strap is 112mm for the long side, 75mm for the short side (doesn't include the buckle of course). So it is on the short side. I wear it on the 4th hole from the tip (ie, the 5th hole if you count from the springbar side).
I measured the strap+watch flat from the end of the strap (buckle side, not including buckle) to the hole I use, it's 7 1/8", I wear watch straps on the loose side. To the last hole it's a shade over 8", so, you should be able to get away with the OE strap on your 7 1/2" wrist.
It's not a bad strap but not pliable at first, it's stiff out of the box. I own nicer straps but this one sure beat the absolute garbage Swatch supplies with this watch:
Inspired by the Model 23, a cutting-edge pocket watch used by U.S. soldiers during WWII, the Khaki Aviation Pilot Pioneer's distinctive design is a tribute to Hamilton's aviation and military heritage.
www.hamiltonwatch.com
I had to replace it since it caused physical pain in my wrist after wearing it for a day, it's that bad.
$99 watches from AliExpress were superior to that supposed "calf leather" strap. Too many 4 figure watches from Swiss brands are supplied with absolute crap leather straps unfortunately. In the case of this Jazzmaster Performer though, it's not too bad.