I have successfully avoided using stabilizer with satin stitch applique by heavily starching the background fabric before cutting. I use a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this solution onto the yardage until it is saturated, toss in dryer, then iron with steam. It gives enough stiffness to the background fabric that stabilizer can be avoided.
You can actually use plain typing paper (the thinner the better) or even printer paper underneath the background fabric as a stabilizer. To remove, you need to use a finger to moisten the stitching from the underside with water, let sit for a minute or two to soften the paper, then pull the paper away from the stitching. I think tissue paper would be too flimsy, although maybe several layers stacked would work. I bought some stitch & ditch paper from Amazon that works well as a stabilizer too. Here is a link to it:
http://www.amazon.com/gp/product/B00...ms_ohs_product