The range isn't the most important thing for the missiles fired from the corvette, but by Norwegian doctrine, it is expected that Skjold class would work as an extended sensor and weapon guidance platform for the Frigates, trough Link 11 and link 16 communication system (Network warfare). (basicly the Skjold class detect and paint the target, for then sending firing order to the Frigates Weapon systems...) I expect the corvette would do the same, but with a stronger sensor platform than what Skjold class have and a tad stronger all around weapon systems... but with commons systems.
in that case, maybe the corvette should just have essm, a good air search set, and CEC to do the engage on remote operation you describe...
Can SM2 actually do that?
if by "that" you mean what @heuhen describes, it's a function of CEC (cooperative engagement capability) called 'engage on remote' where a ship detects and tracks a target, xmits the track data to another ship (w/c is the shooting ship) via datalinks (ie. CEC-DDS), and the shooting ship will launch and perform midcourse guidance for the SM using the remote track data it receives over the datalinks, then perform terminal illumination to achieve intercept (w/ the assumption that after the midcourse phase the target has now moved into the rf horizon of the shooting ship for the terminal guidance phase)...
there's also another capability called 'forward pass' where a ship launches an SM, performs midcourse to bring it in the vicinity of another ship, and that 2nd ship then takes over to perform terminal homing illumination to intercept a target it was tracking (but w/c was not w/in the rf horizon of the 1st, ie. shooter, ship - meaning the shooting ship did not actually detect/track the target)...
if the ships do not have CEC and instead have to rely on link-11/-16 only, then this would be a simpler case of the detecting ship passing it's track data via link-11/-16 to the shooting ship, the shooting ship then
waits for the target to get w/in it's own rf horizon, and then it launches and prosecutes the attack as normal...
it is this "waiting to get target w/in rf horizon" w/c is the diff b/w CEC and regular track sharing via link-11/-16... w/ CEC engage-on-remote it can launch and perform midcourse guidance w/o the need for the target to be w/in the shooter's rf horizon, but the target must enter this horizon by the time terminal guidance commences... w/ CEC forward-pass the target never needs to be w/in the rf horizon of the shooter for midcourse and terminal phase...
(as an aside, if you move up from SM-2 to SM-6 w/ it's active seeker added capability, then even terminal phase guidance no longer needs to be w/in the rf horizon of the shooter for engage-on-remote)