In order to cast a spell, a mage must be holding their spell book and be in physical contact with their focus. Their focus could be a ring, amulet or other object that does not necessarily have to be “held”. As such, a weapon or other object could be held in the hand during spell casting.
A spellsword binds their focus to their chosen weapon as part of the process of becoming a spellsword. As such, as long as they are holding their weapon, they are in physical contact with their focus. In order to cast spells, they would need to be holding their spell book, unless they take the skill “battle casting”, which allows spells to be cast without holding a spell book. The skill also reduces the verbal component of the spells by a number of words and also changes the spell casting verbal, clearly showing their ability to cast without a spell book in hand.