Aye theoretically around 35-36 ohms over a perfect groundplane which would present an swr of around 2:1 in an unbalanced 50 ohm system. Bringing that down to a more acceptable level of swr using the radiator cutting method would indeed throw you off resonance.
The LA8OKA corner-fed delta loop is an interesting antenna. Using a specific ratio of side dimensions you can bring the feed-point impedance down to the 50 ohm mark which effectively gives you the best of both worlds in terms of cutting out matching system losses (by not having to use one) while retaining resonance. I have one up for 20m suspended between two fishing poles using aluminium welding wire for the radiator itself - it's an excellent DX antenna for it's profile.
http://www.arcticpeak.com/antennapag...delta_loop.htm