So long as, at all times no matter which barrel is attached, your serial no on your licence matches that on the gun(ie in your case the receiver), and the caliber is the same, then you are good.

Scwazrh makes a good point, but barrel length is not what will get you here it is overall length of the rifle.
For centrefire over 90cm overall length is non restricted, 90cm and below is restricted, so by having a 16 inch barrel you could feasibly change the status of your firearm to restricted.
Just something to bear in mind but easily measured with your existing barrel.
If the firearm is assembled and is 120cm with the 22 inch barrel then you know you can get a barrel up to 29.5cm shorter and have .5cm to play with for example.