When you plug in your Garmin Edge to your PC there should be a folder called segments on there. Export gpx files of your segments and save the segment gpx in the ‘segments’ folder. I still have my favorited segments from Strava back when I used to pay for premium. They still work offline, no need for an internet connection. This is/was on a Garmin Edge 530 I have since switched to the 1040s so don’t know if it works with that one as well but I can’t see how it shouldn’t. This way the segments are stored on your device instead of synced over from Strava so you don’t need any connection. Report if that worked for you.