HARE KRISHNA
Yes, valmiki Ramayana clearly mentioned that Bhagwan Parshuramji had Vaishnavastra.
Supreme Lord Rama snatched the Vishnubow from the hands of Lord Parshurama and the arrow was already fitted to it.
Raghava, the nimble-handed vanquisher of his opponents, speaking thus in high dudgeon expropriated that estimable weapon, namely the longbow of Vishnu, from the hand of Bhaargava Rama, along with the long-arrow that is already fitted on it. On lifting up the bow that is already fitted with an arrow on bowstring, then Rama started to take aim with it, but being indecisive about the target, then Rama of Dasharatha irefully said this to Rama of Jamagadni.
~valmiki Ramayana Bala Kanda Sarga 76
Lord Rama then himself mentioned that arrow was none other than Vaishnavastra.
"This Vishnu's divine arrow is the conqueror of opponents' citadels, and a vanquisher of their vigour and vainglory, and it will not fall through wastefully... isn't it!" So said archer Rama to axeman Rama. Gods together with the assemblages of sages have come keeping the Grandparent Brahma at their fore, likewise the gandharva-s, apsara-s, siddha-s, caarana-s, kinnaraa-s, yaksha-s, sprites and reptilian beings have also come to see Rama who is now wielding the extraordinary longbow of Vishnu, and extremely amazing event that is going to ensue.
~valmiki Ramayana Bala Kanda Sarga 76