This is the strat on single player…

1) First you tame any expendable flier of any level (for me it was a lvl 44 lymantria)

2) fly to the edge of the wyvern trench, far enough away as to avoid aggravating any belligerent wyvern. There you will place down a sleeping bag and a storage box for food, clothing, weapons, and a cryopod containing an escape dinosaur (for me I used my lvl 120 Argent.)

3) find egg, fly out of the trench and over to the opposite side of where you put your sleeping bag and storage box.

4) let the wyverns kill you and let your sacrificial flier become a martyr for humanity

5) respawn at sleeping bag near the wyvern trench and un-cryo your Argent.

6) once the wyverns that followed and killed you and your sacrifice have dispersed, retrieve your item cache that you dropped when you died and obtain your egg.

7) Fly back to your base and hatch/raise your wyvern, with either wyvern milk or the daedon strategy.

If you use daedon strategy, prepare a truckload of food for your daedon beforehand so that it can heal your baby wyvern.

If you use wyvern milk, either go back to the trench and find a lone female wyvern, grab its attention and shoot it with a net projectile and tranq the freak out of it until it is unconscious. Grab milk and leave. If you are lucky you may find the occasional lone wyvern that spawns outside the trench. Use same strategy here as you did at the trench. The best thing about finding a lone wyvern outside the trench is if you remember where it is, you can come back and repeat the same process.

Thanks to this strategy I now have a lvl 76 female poison wyvern named Petra. Now others can see a relatively easy way to obtain a wyvern egg