Stealing an egg is easiest when two people go one carries the other on the mount. If things get bad the carried person throws the egg on the flying mount and lets go...the wyverns will still chase him and not the person on the mount now with the egg.
The best way to fight alpha wyverns is with a tamed fire wyvern. Because all alphas are fire type, they cannot hurt you with their breath attack (although you can't hurt them with it either) but melee does much more damage anyways
This applies to Ragnarok only:
On the far west side of the Wyvern Trench there are usually an egg or two in the first couple of holes in the wall.
The coordinates (47.0, 51.4) (42.7, 55.4) (44.4, 58.8) and (33.5, 66.8) contain Ice Wyvern eggs. I can confirm the first and last have eggs, while I have only heard that the other two contain them.
Having a couple expendable vultures on aggo seems to help with wyverns attacking your base. The wyvern chases them up high enough that they eventually despawn. Seems the vulture always attacking from above keeps them flying higher and higher. This tactic has saved my base twice from rogue wyverns.
It's important to note that Wyverns of the same elemental type cannot damage or be damaged by the same elemental breath attack, so for instance a fire wyvern is your best bet when alpha wyvern hunting, as it cannot be damaged by its fire breath.