I believe that the Text To Speech program used is Amazon Polly: https://aws.amazon.com/polly/
This is based on an old thread where Fish was talking about the game, back when it was in reeeeaaallly early alpha, and before it was on itch.io.
That thread is here: https://forums.tigsource.com/index.php?topic=69253.0&__cf_chl_captcha_tk__=c3f4d... (The January 21 update for 2020 in particular.)
I think you can use polly for free, but there are limitations for how much you can use the software, and you have to have an amazon account. So if you're willing to create a throwaway account for it, then you should be good to go! I think? I mean, I haven't tried it yet. Maybe tell us how it goes, if you try it.
As for which voice option gets used, I couldn't tell you. If there's a British female preset, then that'd be my best guess. As for getting the audio, I'm not sure if the amazon polly service allows you to directly download voice clips that you create (I'd be surprised if it didn't, but you never know), but you can use a desktop audio recorder to snag the audio as it plays as a workaround. Audacity can do that job well if you're using a more recent version of Windows, and there are a few desktop audio recording apps for iOS, but I have no clue what they're called.