Not very high. I don't have the book with me to quote the exact statistic, but it was under 10%.

The cause of this was that -- despite what war paintings and dramatic accounts may have you believe -- there was very little actual hand-to-hand combat on Napoleonic battlefields. There were plenty of bayonet charges and cavalry charges, but the overwhelming majority of the time, one side would break and run before it came to actual hand-to-hand combat. The main exception was cavalry riding down fleeing foes, but even then the actual casualties caused by melee weapons wasn't very high.

There we rare exceptions (typically during sieges), but for the most part, there just wasn't much actual hand-to-hand combat.

Source: (http://www.amazon.com/gp/product/0300082703?psc=1&redirect=true&ref_=oh_aui_detailpage_o01_s00)