If you emasculate the flower before it opens, bag it after pollination that should help greatly keep contaminating pollen out, although if it didn’t work, no fruit may develop.
Also the pollen spreads better and is easier to apply if you let it dry out first. Anthers can be closed and I find letting them dry they bust open letting the pollen out, or are easy to bust once dry if not open. I still have a hard time getting enough pollen on raspberries as drupes are often missing due to low pollen. It doesn’t matter though, usually still plenty were fertilized. You can see the pollen well too because as it drys it turns a darker color.