no I mustn't/no I shouldn't/no, I don't have to

[navi tasan]

Are sentences "1" and "2" correct in the given contexts and with the given meanings?

Mustn't you send your application today?

1-No, I mustn't. I can wait another week if I want to.
MEANING:
1a-No, I don't have to. I can wait another week if I want to.

================================

Shouldn't you send your application today?

2-No, I shouldn't. I can wait another week if I want to.
MEANING:
2a-No, I don't have to. I can wait another week if I want to.

I think "1" and "2" do not have the desired meanings.

"1a" and "2a" both imply that I could send my application today if I wanted to. "1" and "2" don't have that implication and thus seem to some extent contradictory.



Gratefully,
Navi.

[Tdol]

I'd use needn't. Mustn't and shouldn't don't work well there IMO.