Fighter 1 gives you some nice features: CON saves, weapon proficiencies, a fighting style (dueling or defense, presumably). I would start fighter 1 / bladesinger 6, for 3rd level spells and extra attack, and then see how it feels from there. Action surge is really powerful, especially if you are self buffing and then attacking, so you might want fighter 2 at that point. Shadow blade with a 3rd level slot is probably your best use of concentration for buffing your own offense, but haste gives you a good mix of offense and defense (and with proficiency and +INT to concentration saves you should be pretty much immune to losing concentration for a good while). Although in terms of pure party-wide contribution you're probably better off using your concentration on a control spell like Hypnotic Pattern or Fear (if you take War Caster, you can chase afeared enemies around and hit them with booming blade on AoOs, which is really cruel but powerful).
The Hexblade INT to attack doesn't offer you that much until you raise your INT above your DEX -- you still want DEX for AC (and initiative). But might be a decent option at later levels (after INT hits 20, say). Hexblade's curse is good, particularly if using Haste. Armor of Agathys is nice, but probably not worth delaying wizard levels.