You could also try using pinking shears to trim it. Personally, if I don't have access to the machine to overcast, or zigzag, I carefully use Fray Check. Just be careful not to get it in the center of the linen (although acetone will remove it). Works fine, and doesn't affect the framing after.
You could, as an alternative, iron on something like fusible seam binding - Steam a Seam (light weight).
Just some ideas.
ellice