I would absolutely not wash it in the machine. It's not just the edges that can ravel; every seam can lose threads and create a tangled mess.
What I would do is machine baste it to a muslin foundation and then hand wash.
Edit: Scrolled down and read your second post. You could hand wash as described above in Synthrapol, being sure to use lots of water in the sink and replacing the water frequently if you can see dye in the water. Synthrapol should keep the dye from settling into other fabrics.
What kind of batting do you have? Polyester batting will not shrink. If it's cotton, cotton/poly, or wool the package will tell you if you can prewash. Poly doesn't need prewashing, of course. Cotton batting that is bonded and/or needlepunched can be soaked (as in a washing machine with *no* agitation), spun out, and then dried in a dryer to shrink. Traditional cotton batting cannot be prewashed; it will fall apart in the water.
Lay the whole top out flat to dry, then take off the basted foundation and block to size.