I get good results using volume automation instead of compression across a whole dj mix.  I takes longer, but preserves the original sound much better.  Load your mix into a DAW, and chop the “spikes during transitions” into separate sections or channels, then drop the volume for that section by 1dB, or however much you need.

I use Ableton which makes the whole process pretty quick and painless, but you can do it in Audacity too, which is free.