How do I hide a tubing exit hole in satin without it fraying everywhere?

Skip the fray check entirely. What you want is a hand-worked buttonhole, the kind you'd make on a tailor's lapel. Cut your slit small, whip a thread around the raw edges first to stabilize, then work buttonhole stitch all the way around the slit so every thread end is wrapped. On satin this looks almost decorative, lies flat, feels like nothing, and it flexes with the tubing instead of going stiff like glue does. Practice a few on scraps untill you can do one in under ten minutes, it's just a blanket stitch done close and tight. If you want extra insurance, cut the slit with a stiletto or an awl instead of scissors, that spreads the threads instead of slicing them and fraying basicly disappears. Even better trick though: you may not need to cut the fashion fabric at all. If you make the exit hole through the pocket bag only, the tubing comes out of the pocket opening like anything else you'd carry. Nobody can see where it enters because the pocket itself hides it. I've done this on several dresses and it means zero finished edges to worry about on the outside.

For the bodice, don't run the tubing between the boning and your skin, that's exactly where it'll kink. Corset bodices have a lining layer, so thread the tubing up through the inside of the lining and let it travel in the space between lining and outer fabric. Bones sit on the seams, so keep the tubing running up the middle of a panel, not along a seam line. Tack a few little thread guides or a couple of hand-sewn snaps inside to hold the path in place, because tubing loves to wander.

One more thing: give yourself slack at the pump end. When you sit or the hoop skirt shifts, the tubing length changes more than you'd think. Wear the whole thing around the house for a few hours, sit, dance a little, check the site and the tubing the whole time. Whatever wants to fail will show up in a dress rehearsal, not at the altar.

For my niece's quinceanera dress I had the same fraying nightmare on duchess satin, and the thing that saved me was a scrap of silk organza fused behind the slit before cutting. The satin threads stay trapped in the organza so nothing walks off the edge, and it's so sheer you can't see it from the front. I just catch-stitched it in by hand. Also, on the rehearsal point, my niece wore her dress while we ran through the hall and the tubing caught on a chair arm, which is exactly the kind of thing you want to find out in your kitchen and not mid-dance.

One thing I'd add from making my sister'sprom dress with her CGM transmitter in mind is that the pump itself will pull on that exit hole every time the tubing gets stepped on or caught, so reinforce the back of the pocket bag with a second layer or a small square of self fabric basted behind the slit. Also worth figuring out early wheather you want the pump riding in the pocket or clipped somewhere, because a heavy pump swinging loose in a bag can drag the tubing sideways against the opening all day. When are you planning your first full wear test, before or after the hem is done?