Swapping everything over to road bike

As bash says, a little tool kit would be handy. Jobsworth is just a generic rebranded kit, it is also known at Bikehand, but will see you through everything you need done.

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If I were you I'd buy a box of tools - really makes things easier in the long run. The aptly named Jobsworth tools from Planet X are pretty good value for money I think.

I take it you will be swapping wheels or are you going to be changing the cassettes?

If you are changing them, you with need a Shimano cassette tool and a chain whip.

I don't know why the previous poster is mentioning headsets, that has nothing to do with gearing whatsoever

Everything else is pretty simple. APART from the bottom bracket, because if I am reading that correctly, the Dawes has an integrated bottom bracket with the chainset. So that might be a problem if they are not the same size on both frames.

Headsets require a headset press to fit the cups and crown race, and either the correct tool or a hammer & long drift and a handy guide to plumber's swearwords to get them off the old frame. Bike shop visits are inevitable for this or as in many cases, leave the headset. Integrated headsets like the one on the Specialized are best left in situ.

Removing the crank arms from the bottom bracket axle will require a crank removal tool but every enthusiast ought to own one, so buy one; they are not particularly expensive (less than £10 in some places, but don't skimp, get a good one). Popping the cranks off is a very simple process with this tool. Get the combination type with a (probably) 14mm hex socket built into one end unless you already have a metric socket set in your tool collection.

Removing the bottom bracket is pretty easy if it is a splined one, as per Shimano; you just need the correct splined tool that mates (and a spanner). This is similarly not especially expensive. Even the "old fashioned" BB that is not removed as a single unit, but consists of axle, balls and cups (with two little dints on the outside face) is not difficult to swap out but requires heftier and more expensive dedicated tools to do it properly.
However, upon removing the cranks from both bikes, inspect the length of the bottom bracket axle sticking out on the right hand side (chainring side). If it is the same on both bikes, then you can just leave the bottom bracket bearing unit in the bike frame; simply swap the crank arms.

Pretty much everything else will come off with a small selection of allen keys and spanners.
Replace the brake and gear cable inners and maybe also the chain if it is not in its first flush of youth.