The Wizard's Magical Affinity disadvantage can be entirely offset by the BYSSEPS glyph, or being a Human, making the wizard highly effective at physical combat when maintaining his available enchantments. The Wizard also benefits highly from the already cheap costs of most physical combat glyphs, getting a 50% reduction of mana cost in BYSSEPS, and a 33% reduction in cost of GETINDARE and HALPMEH.
Since BURNDAYRAZ is always generated, finding it is one of the chief priorities for a wizard. Once you do, you'll be in a much better position to fight enemies of all sorts, especially the otherwise-dreaded physical resistant enemies.
Race and Deity Choices
Since wizards are almost completely defined by their magic, it stands to reason that magically-adept races make the best wizards. More importantly, the extra glyph on the map can amount to an extra glyph conversion, assuming you don't play to use it. Elves make for good wizards that can use their favorite spells almost endlessly, while gnomes can turn unwanted spells into valuable mana potions. If you want to have a decent physical attack to fall back on, humans can also work.
Wizards are one of the best-suited classes for Mysteria Annur. This does not mean that Mystera Annur is always the best choice for a wizard, however, since it turns your normally subpar (but still usable) physical attack into a completely useless one. Be sure to convert all the glyphs you don't need before joining her. The magic-hating gods, Taurog and Binlor Ironshield, are naturally poor choices for wizards. The other gods can be useful in the right situations.
Mages do very well in this dungeon. Use your glyph sight to track down BURNDAYRAZ as soon as possible, and you'll have little to fear from the anti-melee traits of the Snake Pit's denizens. BLUDTUPOWA makes your pyromania more efficient, as always. GETINDARE saves mana by letting you use your weak but serviceable melee attack to cherry-tap any nearly-dead monsters without reprisal -- aside from the first-striking Gorgons, of course. HALPMEH will make Serpent-hunting easier until (and possibly even after) you find BURNDAYRAZ.
If you hate watching Vampires inflate their HP at your expense -- and who doesn't? -- then the BLUDTUPOWA glyph is your best friend. The prevalence of Wraiths means that you'll want to rely on a magic-heavy offense anyway, so you'll need to regenerate mana way more than health as you explore. Bear in mind that APHEELSIK and Venom Blades will not work on any of the undead here, so hit-and-regenerate tactics are sub-optimal. For the above reasons, Mystera Annur is a more attractive deity choice than usual, especially if you can find her altar early.
Using BURNDAYRAZ vs Animated Armour helps Wizard beat Factory with Experience Catapult strategy. Since the armours only have one health and don't replenish their death protection, a wizard can even defeat a level 9 one as early as level 1 if they're lucky.
HALPMEH is very useful, especially in the fight against The Iron Man, since his 75% Magic Resistance essentially makes BURNDAYRAZ useless. It's also sometimes more worth it to attack physically and spend your mana on healing rather than casting BURNDAYRAZ. If you can't find HALPMEH, CYDSTEPP would help against The Iron Man, though it's more costly for the other fights.
BLUDTUPOWA helps a lot if you find it early. Since you'll be spending mana on BURNDAYRAZ and possibly HALPMEH for healing most of the time, you'll gain a lot from exploring tiles with this glyph activated.
Other than Elf and Human, you might want to consider picking Dwarf so that you can take more hits during the boss fights.
This can be a tough challenge for the Wizard, because defeating the Library depends on both casting spells and inflicting damage with physical attacks. Going magic only will leave you short of manna when trying to defeat Matron of Flame after first dealing with Aequitas. Choose either a human (and make purchases / deity choices) which boost your health, or choose dwarf and emphasize gaining damage. It is possible to defeat Imps that are 3-4 levels higher than you using a combination of fireball, the HALPMEH glyph, and strategic tile exploration. You must have a deity to defeat this level with a Wizard. The Pactmaker is a good choice if you can get it early. You'll need the extra MANA boon to allow constant healing while fighting the Matron of Flame. Another route for those who chose to emphasize health, would be Dracul, choosing his magic resistance and damage bonus respectively. In any case, be ready to do a lot of retiring and retrying to pass this level.