Maksim,
I don't believe you can. The problem is that the API is "talking to" the cloud back-end (on AWS) not any code that is running locally on the client.
Now, you may be able to figure out a way to locate the particular control and programmatically activate it, but I highly doubt such efforts would be supported and may cease to work as Genesys develop the product.
Another option (and I have no idea if this is even a possibility for you) might be to look at something like Sikulix, this is an automation platform that works graphically, so if your button were able to activate some Sikulix code that located the transfer button and "clicked" it, that may work?
Other than that, I'm out of ideas, I'm afraid.
Of course, as soon as I hit "Post" someone else will probably post how to do it! 🤷‍♂️