The size of mat you have is for 8x10 prints. If you have an 8x10 paper, your normal size border will be about 1/4" on all sides. That will give you 7.5x9.5 size image on 8x10 size paper.

There are several ways of doing this but one way is to shoot with ultimate printing size (aspect ratio) in mind. If you have to work with existing negatives, then your only choices are to find cropping that will work with the image, or as you say custom cut the mat. There are on-line sources that will do it for you relatively inexpensively.