All I can say is I don't really know, but going by what the guy at Hope said about me using an older Pro lever with an M4, that the Pro lever would go close to bar before they worked, I'd suspect that using the newer Mini lever would result in the opposite, the lever would not move much at all with a much harder feel and more effort required to stop.
If you have a newer lever like in the pic you posted, why not connect them up, bleed it and try it out. If it doesn't work all you will have wasted is some brake fluid, your time will have been put to good use as you and us will have learned something useful.
The part numbers for both these types of levers on Hopes' site don't give a clue as to the diameters of pistons in lever. If they are the same diameter they'll work OK but if different sizes they move more or less fluid to caliper resulting in squishy to the bars feel or hard/harder effort with no modulation depending which combination you use.