Here are my ideas on carving wax. as has been mentioned find the wax that has the hardness that you like. I always like to combine that property with a recipe of wax that doesn’t react in a brittle way when carving. A characteristic that gives a smooth sort of texture to the wax. (not really describing this well) Also, I have found the most wonderful tools for carving is a brand called Dockyard. these are made for model makers who work on a small scale, sort of like model ships. There are V-shaped gouges, rounded belly gouges and some other types of carving shapes–my favorite is the 75 degree (angle) V shaped. these are small for the hand. I know several people mentioned the lino engravers and wood block print type tools but I find them way to gross in size for jewelry scaled work. I used to do alot of wax work in my metalsmithing days. Now any carving I do is in dry, unfired metal clay or in baked polymer clay. (by the way, baked polymer clay is an EXCELLENT practice material–those hard waxes are pricey and polymer clay is cheap) I will try to post some pictures of my carving in metal clay and polymer with the Dockyard tools. I also have a short video about how to hold your tool and how to carve in general. One rarely finds information on HOW to carve. Don’t know if I can post this here. My email is bbbsimon@comcast.net if you want to contact me for more info. I have been doing this for years and am happy to advise you. Barbara Simon
bangle in bronze metal clay, carved with Dockyard V-shaped gouge after forming & drying, then fired
Bangle Carved, dry sterling PMC, then fired. using Dockyard Tool 75 degree V-shaped gouge
You can get the same results in hard wax with these Dockyard tools
If you don’t want to purchase the Kate Wolf tools, you can get away with making your own! We don’t do much hand carving anymore (mills and 3d printers are our M.O.), but I still bust out some hand carving to clean up waxes or add details that the mill couldn’t get right.
What I do is whenever I go on a walk around the neighborhood, I keep my eyes on the side of the road, looking for thin metal strips that come off the street sweeper. I’ve got about half a dozen of them now. They’re about a foot long, maybe 5mm wide, and about 1.5mm thick. They’re hardened steel, and can be shaped in to whatever you need, and polished to a mirror finish.
I also occasionally use broken burrs and shape them in to whatever I need at the moment.
Wax carving is rapidly becoming a lost art, so it makes me happy you’re getting in to it! Practice, practice, practice, and you’ll be carving with the best of them in no time 
Ok, I am now determined to find these street sweeper wires!! Who knew??
And thanks for the link to Dockyard tools! Those look gorgeous- definitely ordering some of those!