Hi, i would start by stripping out what you have already. This way you can see what you need and examine health of it all.
17MM and an adjustable spanner will get your lock nuts off, then lay it all out as it comes of. Even better, try removing locknut, spacers and cone from non-drive side only. then, slide rest out of drive side. This way, the exposed axle that sits in frame dropouts will remain exact, in this case a 15/16mm cone spanner and 17mm ordinary spanner will do. A beefy 10mm allen key will remove FHB. they are on tight so attach some kind of lever over allen key or stamp on it, thats just me though
Remove grease guards carefully, they buckle easily and a pain to re-install when butchered up and, can interfere with bearings if badly warped.
Take note if there is a spacer behind old freehub body, sometimes stuck to main hub shell with grease and filth. Normally just refit it, it pushes cassette away from spokes.
When removing axle, be careful of dry bearings bouncing all over the place, assuming you are putting the same ones back! work near floor or bench.
The whole process, i'm sure you will just suss it out. Once all is back to square one and you are tightning non-drive cone and locknut....try leave the axle with a teeny bit of play then, use locknuts either side to take up that last bit of play, it's very stiff but possible with two 17mm's or 17 and adjustable.
Crack on with it, any issues, post back up and we can guide you from there.
Ride yorkshire on an old bike.