If the slates are sound and good for more years of protecting from the weather, they will be removable with care and some skill that is simple to learn, then after valley flashing is properly replaced the slates can be re-installed. Removing and re-installing good slates won't "spoil the whole roof". The pitch of the roof, and size and thickness of the slates, and the length of the valleys will determine the ladders, planks, padding, scaffolding etc he'll need. Don't work up there when the slates are wet - very slippery!
Of course the roof sheathing and rafters are to be checked for soundness and proper nailing. If the slates are all the same size you don’t have to keep them in order of removal. You're wise to get some more sound slates, new or old, closely matched in color of the same thickness and the same size or larger to replace a few you might break. Hold a removed slate up with one hand and tap it lightly on a face with a hammer. If it rings it's good, if it thuds it's mush and is good for roadbed material.
I prefer to make valley flashing pcs of 24" x 10' cold rolled (hard) copper or lead coated copper, 16oz or 20 oz per sq ft. I'll use lead sheet, 2.5lb or 4lb per sq ft for step flashing or chimney counterflashing or cap flashing and pans, but very rarely for valleys. Lead is available 4' x4' and 4' x5'. It is dense and easy to form, but doesn't hold to a bent profile like hard copper will. You can bend the lead by hand (wear gloves and wash your hands before you eat lunch) but you'll need a brake to bend the cold rolled.
Pull out all nails that held down old valley flashing. Install 30# felt in the length of the valley, fasten w copper nails. Valley flashings to be bent in the shape of a W, with hems at the outer edges. The inverted ^ at the center has 1" legs and it sticks up to the sky, allowing expansion/contraction of the metal. Then the wings or outer legs of the W lie flat onto the roof planes and are c. 10" wide. The outside edges get another bend, or hem, 3/4" - 1" wide (the entire 10' length) inward onto the top (sky side) of the 10" wide wings c. 180 degrees but not closed tight. This prevents water from running beyond the edge, plus cleats hook into it at 12" oc to hold flashing in place and to have NO NAILS PUNCTURE THE VALLEY FLASHING except one copper nail at each top corner to hold it. Cleats are same metal, 2.5" x 4" and are nailed w (2) copper nails to the roof deck just outside the valley, one end bent as a tab to grip inside the hem, the other end tab bent up, over, and flat down to cover the 2 nail heads.
Just as the metal flashing is to be installed, roll out red rosin paper to isolate the metal from the felt ("tar paper") so flashing metal will slide/move rather than get cemented to the "tar". The next flashing sheet up the valley overlaps the first by 6" with its hems inside the hems of the 1st sheet. Keep the water in the valley and flowing downward, right?
This new work should have no need for caulks or mastic or roof cement. To temp repair an existing leaking valley (or around chimneys) these rarely are 100% effective regardless of how much is gobbed on, unless you can see the damaged areas of eroded and corroded lines , tears and pinholes in the metal and fill and seal them. Re-do annually until you can afford to properly re-flash.
Two books w rules, specs, pics and drawings: "The Slate Book" and "Copper and Common Sense".
If you have to buy new slates any N American slate will be good for 100+ yrs, except PA slate good for 50 yrs - not worth the slightly cheaper price IMO.

Tools: you'll at least need a slate ripper, and good to get a slate hammer. New or used made by Stortz Co Philadelphia PA are excellent. If you have to cut or trim slates as you install them over the valley flashing sides you'll need a slate cutter. Nail holes are best "punched" rather than drilled. Punch holes from the back of the slate, using the slate hammer point or a nail set as a fine punch. Slate cutters usually have a punch point too. Slates hang on two, and only two copper nails, HUNG, not nailed down tight. A wide tipped flat bar is very useful. I am still using my 35 yr old American made Stanley Wonder Bar. So much better than the recently Mexican made, or is Stanley having them made in China now ? - prob worse.

Normal overlap of next course is Exposure plus 2" (e.g. 9" exposure requires a 20" long slate). Wear gloves and a respirator when removing existing slates and vacuum cleaning or sweeping existing felt and/or roof deck. Wear tough old pants and sneakers or boots w rubbery soles for a good grip. Prepare to get real dirty. Like most good quality construction work it's the 3 Ds, Detailed, Dirty and Dangerous. Could we add Difficult? not if you follow the rules and are prepared.
If you work smart and safe you'll have no need for good luck, except for the weather, and we can't do anything about that.

Glad to be of help Richard. I appreciate your hosting us at TTRAG in Morristown and Upper Canada Village. I learned lots at the Conference and tours. I still play one my Bobby Watt CDs every week.
Steve Miller

Shine on!