You will need to use acid dyes rather than fiber reactive dyes.
But you can also use fiber reactive dyes as acid dyes. You just have to use an acid, such as white vinegar, instead of soda ash, and use more heat. It is best to steam-set the results, as the room-temperature recipes might not produce the color intensity you want.
Wool takes color quite well with the soda ash recipe, but the high pH damages it badly. The low pH of the acid dyeing recipe protects the texture of the wool, which is very important.
Paula