Actually, there is something you can do to improve the outcome over always accepting or always switching, without knowing the distribution of money.

All you need to do is define your probability of switching according to some function that decreases as the amount of money in the envelope increases. So for example, you could switch with probability exp(-X), where X is the amount of money in the envelope you start with.

Of course, to have an exactly optimal strategy, or even to know how much that general strategy will benefit you, you would need to know more about the distribution.