Short answer.
Yes you can do it, but please do not.
Long Answer
Can I do it?
Yes, of course you can.
Simply fetch the data from the backend and do a find-replace on the string for any words you want spoken differently using a dictionary of words to replace, then add the new version of the string as the accessibility label.
SHOULD you do it?
Absolutely not.
Every time someone tries to "fix" pronunciation it ends up making things a lot worse.
I don't even understand why you would want screen reader users to hear "speak" whenever anyone else sees "speech", it does not make sense and is likely to break the meaning of sentences:
"I attended the speech given last night, it was very informative".
Would transform into:
"I attended the speak given last night, it was very informative"
Screen reader users are used to it.
A screen reader user is used to hearing things said differently (and incorrectly!), my guess is you have not been using a screen reader long enough to get used to the idiosyncrasies of screen reader speech.
Far from helping screen reader users you will actually end up making things worse.
I have only ever overridden screen reader default behaviour twice, once when it was a version number that was being read as a date and once when it was a password manager that read the password back and would try and read things as words.
Other than those very narrow examples I have not come across a reason to change things for a screen reader.
What about braille users?
You could change things because they don't sound right. But braille users also use screen readers and changing things for them could be very confusing (as per the example above of "speech").
What about best practices
"Give assistive technology users as similar an experience as possible to non assistive tech users". That is the number one guiding principle of accessibility, the second you change pronunciations and words, you potentially change the meaning of sentences and therefore offer a different experience.
Summing up
Anyway this is turning into a rant when it isn't meant to be (my apologies, I am just trying to get the point across as I answer similar questions to this quite often!), hopefully you get the idea, leave it alone and present the same info, I haven't even covered different speech synthesizers, language translation and more that using "unnatural" language can interfere with.