I would not pair that amp with those speakers regardless of power. They both skew to the bright side in the treble region and together may sound like nails on a blackboard. If you share your budget and the other equipment in your system you’ll get some much better recommendations here. Just my $0.02 FWIW.
Classe is known to have good synergy with B&W and they’re frequently sold together for that reason — B&W even bought Classe back in 2001 but I believe they’re now both owned by Sound United. Here’s a nice pre and amp a bit over your budget but worth stretching a bit for IMHO.
The amp puts out 100Wpc but doubles down to 200Wpc @ 4 Ohms so should be fine. More power would likely help, but at your budget that might be tough. Hope this helps, and best of luck.