I do have one of those floor corkers (but not a champagne corker) and that's what I use. The problem is you still have to do some manipulating because they are designed to fully cork bottles, not to leave some cork out as for champagne. I'm not sure if you would be able to cork bottles very well with a 2 arm type corker. I have used those for wine before and found it difficult to control the cork depth (even when i was only trying to push the cork completely in). So I think you do need a floor corker, but not necessarily one designed for champagne.
This system does work for a coronna corker, though it is definitely easier on the floor corker. Depending on how popular wine making is in your area, you might be able to find a floor corker on craigslist. It looks like portuguese floor corkers are about the same cost as a coronna corker/capper and I would suggest going for something like the former over the latter if you decide to go for something in that price range.
Here is the link:
http://horscategoriebrewing.blogspot.ca/2013/11/corking-your-homebrew.html