The software is critical. You can mouse and keyboard your way through the rest. One thing I think is a must is soundcard that has two outputs or can be hacked to play two outputs, one in each channel. Mixing is a lot easier if you can monitor the output and have an ear on the grunt work as well.
I made a mix on a bootleg version of Traktor (I think) years upon years ago. It's pretty good if you have a basic understanding of music (really just tempo, understanding a HP and LP filter, and pitch/key... even then really just being able to notice if two songs are clashing... but I've heard shit on the radio that doesn't even get that right so maybe it's not super critical).
Software is the most important thing ( I use traktor ) lots of people use serato. The Hardware just gives you that hands on feel. But like Somebody else said you can just record off traktor using a mouse and keyboard
If you know what you're doing its possible to use virtual dj, which is free & use a mouse...you'll need to use sync ofc - not sure if virtual dj has that?