You can change the runway down to a late stage of the approach - ie. 700 feet. At 700ft RA with APPR mode engaged, the ILS course and frequency are locked into the receiver. Nothing you do will change them. At 400ft RA - LAND mode engages and the only way you can get out of it is either to go around, or disconnect the AP/FD.
I'd agree with Nigel though - do you really want to be having your head down and fiddling about that late on? Just take the AP/FD off and fly the aeroplane! Assuming you are sidestepping to a parallel runway - you'll even get GS mini. If you're IMC - get the other guy to hard tune the new ILS and follow that if you have time - if you're too low for all that and IMC - go around.
Hope this helps!