The key question here is how are the photos saved; is there a removable memory card in the drone (i.e. microSD)? IF there is, then there are lots of options for data recovery. The important thing is to not use the card until you are ready to try and recover the data.
It sounds like the data recovery is logical in nature so you can try yourself by suing tools such as R-Studio or DDRescue. If you are uncomfortable doing this or don't want to invest in these tools for a one-off data recovery, then consider a professional data recovery lab. Logical data recovery is not that expensive...relatively speaking.