On element orders in covers of finite simple classical groups

We show that finite simple symplectic groups of dimension at least 6, finite simple orthogonal groups of dimension at least 7, and finite simple unitary groups of dimension at least 4, except for U5(2), have the following property: If such a group G, defined over a field of characteristic p, acts on a vector space over a field of positive characteristic other than p, then the corresponding semidirect product contains an element whose order is distinct from the order of any element of G.