Does a mayonnaise have longer shelf life with egg white only as opposed to yolk?
There is no difference in the shelf life of mayonnaise made with egg whites, or egg yolks, or whole eggs. Since you are using pasteurized eggs, this counts as a standard cooked dish, and the shelf life is 3-5 days in the fridge. It would be 1-2 days for raw eggs. 

You cannot evaluate the safe shelf life of a food by yourself. In principle, one could commission a microbiological study to prove that a given recipe is somehow longer lasting than one would expect from its general category. That is likely to cost more than hiring a cook to make you a daily batch of mayonnaise for the next few years. 

For more information on food safety, I would suggest that you also look at the extensive information we have compiled on the topic: https://cooking.stackexchange.com/tags/food-safety/info