A minidish LNB is specifically designed to focus on the full area of the oval shape dish. If you use a conventional LNB with a 40mm neck adapter, the performance is likely to be poor, because it focuses on a circular area, resulting in "drop-out" during bad weather. Beware sellers of twin-output LNBs. Only a few were ever made for the Sky minidish so, if you see one for sale, it might be a conventional LNB with an adapter to make it fit. It might not even point accurately at the centre of the dish. Also beware of any LNBs which seem too cheap. You know the old adage - "if it seems too good to be true..."
To remove the old LNB, pull out the plastic pin that holds the spigot to the dish arm (if fitted). Place a protective piece of thick card or wood against the widest point of the LNB (the part facing the dish) and strike it hard enough to knock the spigot out of the dish arm. Unscrew the 'F' plug from the old LNB and look inside for signs of water ingress which will make the copper turn green or black. Any sign of water indicates that the entire cable run should be replaced.
Screw the 'F' plug to the new LNB and tighten gently with a 10mm or 11mm spanner. To reduce the risk of water ingress, and to lubricate the threads, you can apply silicone grease. To further reduce the risk of water ingress, fit rubber "boot" sleeves or use self-amalgamating tape to seal the 'F' plugs. Plenty of web sites show you how to do this. Just search for "How to fit an F plug" or similar. Provided that you haven't moved the dish at all, the new LNB should work straight away. However, because of the extra cable weight, the dish arm may start to sag after a day or two and the result will be missing channels. To prevent this effect, you can fasten a length of strong fishing line or steel wire to a hole in the top rim of the dish and tie it around the LNB to add support. The thin wire or line will not affect the signal.
The "skew" (twist position) of the LNB is important. Set it to about "twenty to three" looking at the front face of the dish. Make final adjustments by observing the "signal quality" in the on-screen menu of the Sky Digibox.