How many colors are you using in your design? If it's only 2 or 3 then it wouldn't be too much of a pain. You could practice on a large square of material to see if Batiking it would work for you. I wasn't thinking about carving blocks for block printing...I was thinking you could start by drawing your design (w/pencil) on a large square of the lightest color material you plan to use in your design. Stretch your material out by stapling edges to a wooden frame (at least 2 opposite sides). With assorted size artist paint brushes or Batiking tools you can paint the hot wax on the part of the design that you would want to remain the light color (be sure the wax penetrates thru the material for the best wax resist) & then dip the whole square into a cool dye bath of your next color. Always dye your lightest colors & graduate with each step to the next color in sequence from lightest to darkest. After the next color dries, then you could wax the part of the design that you want to stay the 2nd color & then dip into your final darkest color for the last dyebath. You can crinkle it a little while in dyebaths if you want a crackled look.
Make a double boiler (if you don't have one). I used to put beeswax in large metal cans or use an old cast iron coffee pots & stick the cans or coffee pot in a large cast iron frying pan & then pour water in the pan around the cans or iron pot (thrift stores usually have these items cheap. My mom never wanted me to use her good pans. :( Be sure to check your water level so that it doesn't run dry & cause the wax to get too hot. Beeswax is more expensive & works a little better but I have had good results with parafin wax also. You would want to use an old iron (from a thrift store?) also. I use news print on top of the batik to iron out the wax. Watch carefully so that the print from the news paper doesn't transfer. I always used black & white print & usually always around & available. This is just one idea but not sure what your design is. Someone else may have another idea for you that would work better. Good luck with your project. It is a challange & you will figure it out. :D