How Do I Shorten the Pull Distance on UIRefreshControl to Activate the Pull to Refresh Action?

you can still use refreshControl but with some modifications!

add these code to your viewController:

var canRefresh = true

override func scrollViewDidScroll(scrollView: UIScrollView) {

    if scrollView.contentOffset.y < -100 { //change 100 to whatever you want

        if canRefresh && !self.refreshControl.refreshing {

            self.canRefresh = false
            self.refreshControl.beginRefreshing()

            self.refresh() // your viewController refresh function
        }
    }else if scrollView.contentOffset.y >= 0 { 

        self.canRefresh = true
    }
}

and as usual in the end of your refresh logic in self.refresh() function add :

   self.refreshControl.endRefreshing()

As per the Apple Docs, I don't see any way to modify UIRefreshControl parameters.
link: https://developer.apple.com/library/ios/documentation/uikit/reference/UIRefreshControl_class/Reference/Reference.html

Use a third-party component like ODRefreshControl (to customize the scroll-distance in order to activate the refresh, modify the #define kMaxDistance constant).

or...

Don't use the UIRefreshControl and instead implement your own logic in the -scrollViewDidScroll method like:

- (void)scrollViewDidScroll:(UIScrollView *)scrollView
{
    if ((scrollView.contentOffset.y + scrollView.frame.size.height) >= scrollView.contentSize.height) {
        //refresh logic
    }
}