"Air dry clay" is such an unspecific word used for so many different products that it's impossible to tell which one you have or what to do with it. The only sure way to make it firmer is to let it dry for a while (like 30 minutes) and then knead it thoroughly to even out the moisture content. Repeat until you have a consistency you can work with.
Instead, I propose buying a product that is designed for sculpting purposes or make your own.
Store-bought products include the two part putties you mentioned, but you could also use polymer clay (the kind that gets hard when cold and has to be warmed in your hands first) or wax designed for sculpting or mold making.
One DIY modeling paste that seems to be very popular is called "cold porcelain". It has a very smooth texture, which makes it well suited for modelling, but it dries very hard. However, cold porcelain shrinks while drying, so it may not be ideal for your purposes. See recipes and my personal experience in this related answer.