if you remember that the 9,3x53R Swiss is the rimmed 9,3x53 which is not more than a 7,5x55 necked up to 9,3mm the swiss and the finnish case are surprising close to each other. you have to reduce the rim thickness on Sako brass and blow the neck out with a fireform load.

iirc, the rim thickness is max 1,60 mm on the finnish case and 1,10mm max on the swiss case, the neck is 4mm forward on the swiss case

many owner of swiss rifles use Sako brass for handloading with the little benefit it have the right headstamp also.