Send updated manuscript before referees' response

There is nothing you can typically do during review -- the reviewers have received their copy of the manuscript that they were asked to review, and as an editor I would leave it at that even if I got an updated version. My response (in different words) to the author would have been "Well, these are things you should have thought about before submitting the paper."

But assuming the first version wasn't terrible, you will get the opportunity to roll your changes into any revisions you make in response to the reviewer comments.

I think there's room for negotiation, or for a query.

Write the editor describing the changes. Note that they improve readability but don't really affect the results (assuming that's the case). Do apologize for not having caught typos before submission.

Then ask the editor whether s/he wants to send the revised version out, or wait. If the papers went to referees just a little while ago they may not have started work and the editor may decide to send on the revisions. It's the editor's call.