You can do one of two things:
Make a copy of your snippet - that does what you have coded in reverse - and store it in your skuid page as a “generic JS” (Create a new one of those resources to see the boilerplate code that triggers the snippet on page load).
Build an event triggered action sequence that runs on the Skuid Page: Rendered
event. This sequence can update the value of your UI only field with the value from the real one.
This Synching is always a problem with using UI Only fields as a proxy for the real fields in a database. Sometimes there are good reasons for doing this, but as a rule it is going to be more straightforward to simply add the underlying field to the page and have users interact with it. Maybe you can explain a bit more why your are using the UI only field here?