Bladesinger - please help with character progression going forward

Hey all, title just about sums it up.

My character is a Shadar-Kai Bladesinger level 7. I'm playing it more like a martial than a wizard and I currently feel very, very effective. I'm kind of a party frontline which I know won't be sustainable in the future and I might just die, but for now it works very well. Most of the time I start off the combat with Bladesong + either an offensive damaging spell like Lightning Bolt or a defensive like Mirror Image and at 2nd round I'm going in melee with Shadow Blade or Spirit Shroud.

Full stats and items:

STR:8 DEX:18 CON:16: INT:19* WIS:14 CHA:10

Rapier +1, Studded Leather +1, Headband of Intelligence (I was allowed to dump INT to use the headband if I wanted), Feat: Elven Accuracy (we're playing with slightly nerfed flanking rules, which makes the advantage not as common, but it happens often enough for this feat to be very useful)

If I wanted to multiclass now (level 8) I'd be allowed to change the order in which I chose the class levels, meaning I could start as a Fighter, for example (part of the conversion to new rules and classes, one time deal only). How bad of an idea is that? Con saves proficiency, Weapon Mastery (in this case Vex would allow me to use Elven Accuracy even more often, but I'd probably have to use Spirit Shroud more often, since Shadow Blade doesn't have a weapon type), Fighting Style. Sounds fantastic. I'd lose out on spell progression and I'd delay my feat. I don't think I mind waiting an additional level for spells, but feat hurts a bit.

My spells mainly consist of most available rituals and notably: Shadow Blade, Spirit Shroud, Lightning Bolt, Mirror Image, Shield, Absorb Elements, Polymorph, Gravity Sinkhole, Steel Wind Strike (homebrew; deleveled with added scaling). List is fairly selfish with no battlefield control spells, but that's how I wanted my blade wielding Bladesinger to be (I played a control wizard before but he died, needed a change).

So with all that said. Should I dip (or start rather) a Fighter level now, or should I continue as Wizard? Maybe a traditional, non start dip later is a better idea? Like at level 10 or something?

Sorry for the wall of text. I'd appreciate your thoughts and thanks for reading.

Edit: We'd also get Origin feats with conversion. I'd probably invest more into my survivality, so I'd pick Tough, although Alert and Lucky are tempting as well.