According to the answers given here, a SannyAsi can perform Vedic rituals even after taking SannyAsa.
Now, the first purificatory rite that precedes all Vedic rituals is the act of sipping water called Achamana.
And, according to the following verses from scriptures, Achamana successfully purifies the performer only when it is performed with the Upavita on and with the SikhA tied.
A twice-born, who stands without washing his feet, or who performs the Achamanam without binding the tuft of his hair on the crown or without putting on his sacred thread, is impure. (15)
Samvarta Smriti's Chapter 1.
One must always put on the sacred thread and bind the tuft of hair on the crown : what one does without having the sacred thread on or without binding the tuft of hair on the crown, is equal to an act not done.
Katyayana Smriti's Chapter 1.
But, a SannyAsi does neither have a Upavita nor a SikhA. Then without them how is he able to perform the first purificatory act?
Now, there is some Upanishad which says that the Self is the Sacred thread for the SannyAsi. Ok, but what about the SikhA?
Question- If Self is the substitute for the Sacred thread, what substitutes for the SikhA for a SannyAsi given that he does not sport one and also given the fact that he is allowed to do Vedic rituals?