Is it risky to initiate a wire transfer that includes currency conversion from USD to EUR during a weekend because of a volatile Mondays exchange rates?
It really depends on the event risk that day. There is typically some weekend gap risk involved with currency exchange rates, but the hard currencies typically do not see extreme volatility over the weekend (hence the hard currency label).
I work for a foreign exchange broker and any wires initiated over the weekend are filled at the best available Monday price. The weekend gap risk should not affect you unless you are holding a forward contract with your FX provider.