You can't use rim brakes (without a major bodge) because the rim on 700c wheels will be in the wong place.
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Both the bikes in the links i've posted are using exactly the same set of 700c disc wheels . (Commonly called 29er or hybrid wheels). The Black bike is a Rock Lobster was designed for standard 26" wheels, whereas the second is a Kona 2-9was designed specifically for 700c wheels.
The CL rotors don't cause too much of an issue. You just need to get the correctly sized shimano rotor for your new wheels (as in 160/180). It doesn't really matter if the new rotors are CL or 6 bolt.
Just for the record, would running a narrow (1 inch/1.25 inch) tyre on my standard rim be a big difference from running a true 700c wheel?
Yes. The main difference will be the gearing.
With a 700c wheel the circumfrence of the tyre will be larger therefore all your gears will be higher.
Also the smaller the wheel the smaller the contact patch of the tyre. The smaller the contact patch the more the tyre needs to deform and therefore the higher the rolling resistance. Simply pumping the 26" tyre up to a slightly higher pressure could easily compensate for the smaller diameter but by doing so you'll make the ride hasher.
The 26" wheels should in theory be lighter and they should accelerate and climb better though