AFAIK, any act done without wearing the upavita and the sikha tied is like an act not done. These are the first prerequisites and there are obviously few others as well.
Now, the doubt arose in my mind after seeing what Chanakya did.
Chanakya is said to have taken an oath to leave his śikhā untied until he humbles the Nanda kings who insulted him.
Then being a Brahmin, how was he able to perform his daily rites and other rites for so many years?
Note that, here my question is not exactly how Chanakya did his nitya karmas with sikha untied but generally is it possible at all to do so? Are there any shortcuts given in the scriptures?