Sure, but then you cannot use TWF and have a second chance to apply your SA.
If you go rapier your CA will be disengage. If you go twin shortsword, you can TWF instead of CA with your bonus action and still move out of range. That'd also means you'd have to sheath your offhand to cast a spell.
Check which spells you will take and see how often will you need a good spell DC. You may want to reduce to Int14 and bump Wis12 / Cha10, or bump one and get Con15 for resilient (Con).
The bladesinger dip is a good plan. If you later want more magic, you won't lose any damage since level 6 extra attack compensate for the lost 2d6 SA.
You should race to Dex20, since it's your damage and AC.