I don't think so, I believe it's just the female but I have another mod running with EC so on my server all wyverns do

Is there a specific area on the map does the eggs spawns? We are playing on the center map.
Also, can we kill the alpha wyvern first before we look for the egg?

Many thanks!

And one more, if a female alpha wyvern spawns is it 100% chance of alpha wyvern egg?

The mechanic never worked perfect. Normaly, only females should lay eggs, and if i remember right... if a nest spawns (happens not everytime), the nest with the egg should spawn on the ground together with the wyvern, so you can find eggs on every place with wyvern spawns. What i`ve seen, is that only the female thing is fixed an male wyverns no longer spawn eggs. The other parts of the mechanic is buggy. Female wyverns can spawn eggs with or without nests whenever they land, normal wyverns often spawn multiple eggs together. Sometimes i saw a killed wyvern falling to the ground and an egg spawned under the dead body. And all those eggs might spoil over time, but like rock drake eggs they never disappear after the spoiltimer is zero so the map becomes an egg dump over time xD.
So at the end: Buggy mechanic never competely fixed, and no, there seems no 100% chance for an egg to spawn. What i did a few times is following female alpha wyverns with a safe distance and waited for them to land over and over again until an egg spawns .

the mod is amasing

What LoneWolf said is correct.

Yes the mod spawns Alpha & Normal Wyvern Eggs on The Center. It's quite buggy but works. The eggs usually spawns where the FEMALE Wyvern lands. Alpha Wyvern Eggs will also be most likely on a large red nest that you could see from quite a distance.