Steam a Seam is heavier than most fusibles (probably not Heat & Bond, but everything else for sure). It also requires one of the longest pressing times. I never had much luck with it, but in fairness, I haven't used it in many years & perhaps back then I didn't realize that to add fusible it was critical to only use up & down movements to press & not iron side-to-side at all. I always had wrinkles in those projects and haven't gone back to it since.
Steam a Seam Lite is much lighter, but still requires one of the longest pressing times. For example, with Pellon 805 WonderUnder, you quickly tack the fusible to the applique (5 sec max) and then press the applique to your backing fabric (10-15 sec). SaS Lite has you stick it to the applique & the press to the backing fabric for 30 seconds.
The best product I could think of for doing an applique with silk ties would be Misty Fuse. It is the lightest weight fusible on the market & fuses at the lowest temperature. I've used it with silk organza & it is not even noticeable in the end. Because it is designed to fuse on the lower heat setting, it should adhere better to the silk... which should help reduce the number of wrinkles in your next project.