Well, I've heard that acrylic soakers do exist, but unlike wool ones they need to be washed regularly. They don't have the antimicrobial aspect that wool does, so they get stinky when they get wet. I've never used an acrylic soaker, but I've heard others say they work OK. My guess would be that they're not as absorbant either. Most of the folks who I've read of using acrylic though use a wool/acrylic blend.
Just out of curiousity, why don't you want to use wool soakers? I realize you're a vegan, but I didn't know that meant you used no animal products at all. Thought it was only those that hurt or kill the animal (like leather, fur, etc.). I have several friends who raise sheep & make wool and it doesn't hurt the sheep in the least. In fact, it's good for them. You can even find "organic" wool from sheep who are allowed to free range & not fed with animal by-products.
Anyway, hope this helps. I'm sure more experienced mama's will be able to give you some links to places which make acrylic soakers. Good luck!