Why not just use the Chrome iOS app?
As mentioned in the post, I hate it - without a doubt the worst UI google have released today. Plus you still cant set it as a default browser in iOS. Dealbreaker x2.
Google will need to update Chrome on iOS and desktop to support Handoff, but it is a public feature so it's just a matter of will, time, and priorities.
Someone more knowledgable can tell us if this is even possible. But hopefully the idea makes sense...
I'm confused - are you saying you want an app that allows you to open tabs in Safari on iOS that you have open in Chrome on desktop?