Does "pro rata" need a preposition?

If I wanted to make this totally clear and unambiguous I would use

... will be distributed pro rata based on number of shares held.

In this sentence, pro rata is an adverb.

The preposition to that you have suggested links to the verb distribute. With this verb, to links to the target of the distribution and typically the preposition by introduces the manner of the distribution.

distribute food by truck to a Somali refugee camp

You could say

will be distributed pro rata by shares held.

however, I want it to be clear that by matches the verb rather than the adverb.