The 3e sourcebook *City of Splendors: Waterdeep* features (from page 33 on) a description of the various armed forces associated with the city:

>The Lords of Waterdeep enforce their rule and maintain peace and security through the city’s armed forces. Waterdeep’s defenders are divided into four branches: the Griffon Cavalry, the City Guard, the City Watch, and the Navy. The Gray Hands act as an elite company, called in for emergencies.

 - The griffon cavalry number just a hundred members, and by class mostly aristocrats, fighters, paladins, rangers and warriors (aristocrat and warrior being less powerful NPC classes).

 - The City Guard are given as numbering 1,200, but the texts notes that the membership can swell to as much as 12,000 in war-time, the numbers being bolstered by hiring mercenaries. The associated classes of the organisation are barbarian, cleric, fighter, paladin, ranger, rogue, and warrior.

 - The City Watch number 1,600 members, including the classes of cleric, expert (another NPC class), fighter, paladin, ranger, rogue, sorcerer, warrior, and wizard. Specifically regarding your interest in the magic-users, the Watch has one squadron of a half-dozen wizards/sorcerers led by a "Senior Watch-Wizard" per ward, of which there are 7 (or 8, if the waters of the harbour also count) - so there's a low proportion of arcane casters in the membership, even allowing for some number outside those squads - probably no more than 5% at best. It's not clear what the distribution of divine casters such as clerics, paladins and rangers is.

 - The City Navy has a standing membership of 2,000, but as the Guard, in wartime the ranks can swell to as much as 9,000 by the addition of merchant sailors. The associated classes are barbarian, bard, cleric, expert, fighter, ranger, rogue, and warrior.