The Egg Salad sandwich is to sandwiches what the Hawaiian is to pizzas. It doesn’t matter how many guests you have, how many sandwiches, or how many types of sandwiches you serve, if you have egg salad sandwiches you are going to have a bunch of festering warm egg salad sandwiches lying around at the end of the party. In the history of parties and get-togethers, there has never been a single recorded instance of any kind of social event where egg salad sandwiches were served and not left over. If you want to serve an egg based food at a party then bake a cake.
Eggs are meant to be eaten hot off the pan with bacon or ham in the mornings. They are not meant to be mashed up with mayo and left lying around at room temperature for hours. I like eggs and eat them all the time, but that does not blind me to the fact that egg salad sandwiches are disgusting, and become increasingly so every minute that they spend lying around in an overheated living room on a Sunday afternoon.
I understand the temptation to make these awful things. They are inexpensive and easy to make; you can whip up a hundred sandwiches in 10 minutes with a jar of mayo, a dozen eggs, and a couple loaves of Wonderbread. And if you are planning the type of afternoon social gathering that lends itself to sandwich trays, there will no doubt be a 60+ year old woman who loves egg sandwiches who has taken an active role in the planning of said social gathering. She will almost certainly offer to make a hundred sandwiches for you, which will help her feel like she made a great contribution of a hundred sandwiches. You certainly don’t want to be ungrateful or unappreciative, but this situation can be easily diffused by saying that someone at the party has an egg allergy. If you don’t want to run the risk of being caught out in that lie, just say that you already bought a pile of ham on special and ask her if she wouldn’t mind making them for you. That way she gets that satisfaction of helping without having to spend any money. It’s a true win-win.
If you are going to serve sandwiches at a party just stick with some combination of grocery store sliced meat. Cured meats like ham and salami would be at the top of the list since they are designed to be able to lie around in a warm living room for a while, but the reality is that all grocery store sliced meats are well salted and will hold up just fine no matter how long your gathering drags on. To be on the safe side, this might be one of those times when you might want to avoid the more expensive versions that claim not to use preservatives.