After measuring I think that the most I could get away with is around 140mm.
So as a follow up question, is the cooler you linked the best value, small form factor cooler? Or is there some others I should consider, otherwise I'd have to spend around $80 on a case. (probably this case after researching, https://www.amazon.ca/Corsair-Carbide-200R-Compact-CC-9011023-WW/dp/B009GXZ8MM/ )
Thanks for the help, it's much appreciated