But really, wouldn't the solution be to create grenadier corps? Mixed arms units were all the rage in Early Modern Era Europe. Just look at the Spanish Tercio or the British Grenadiers. Even Sweden got in on the fun with Gustavus Adolphus' use of combined arms and light cannons (which Napoleon took and perfected).
Just use the grenades AND the sword. Roman Legionnaires were packing a pilum, a gladius/spatha, and a shield all at the same time. Surely you can manage some fraggies and a baggy.