Actually for a Vaishnava it's better to go for a Vaishnava Guru. And, the same for others.
Quoting Lord Shiva's words from the KulAchudAmani Tantram:
UdAsino hyudAsinAm vanastha vanavAsinah |
YatinAncha yatih prokta
grihasthAnam gurugrihi ||
Vaishnave vaishnavo grAhyo shaive
ShAktike vidyAd dikshAswAmi na samshayah ||
An UdAsina should accept another UdAsina as his Guru, a forest-dweller
a forest-dweller, a Yati (an ascetic basically) a Yati, a householder a householder, a Vaishnava a
Vaishnava, a Shaiva a Shaiva. But in ShAkta DikshAs all of them (i.e a ShAkta, Shaiva and Vaishnava) can be
the Guru (DikshAswAmi).
BTW, note that I am not discouraging you from doing anything.
Meaning of "Vaishnave Vaishnavo grAhyo" --- In Vaishnava DikshA (Vaishnave) a Vaishnava Guru (Vaishnavo) is acceptable (grAhyo).
A Vaishnavo Guru - One who is part of a Vaishnava Parampara by DikshA; one who is practicing Vaishnava SAdhanas and Mantras.
This website says that the 9 NAthas are Lord Vishnu's avatAras.
Kavi Narayan as Machindranath
Hari Narayan as Gorakshanath
Antariksha Narayan as Jalandharnath
Prabuddha Narayan as Kanifnath
Pipalayan Narayan Charpatinath
Avirhotra Narayan as Nagesh nath
Narayan as Bhartarinath
Chamas Narayan as Revannath.
“Karbhajan Narayan” as Gahininath.
A similar verse from the MahAnirvAna Tantram's chapter 10:
ShAkte shAkto guruh shastah shaive shaivo gururmato |
vaishnavah saure sauro guru rudAhritah ||
kaulah sarvarta sathguruh |
For the ShAktas (devotees of Shakti) a ShAkta Guru is recommended, for
the Shaivas a Shaiva Guru, for the Vaishnavas a Vaishnava Guru and the for the
Sauras (devotees of Surya) a Saura Guru is apt. For the GAnapatyas, a
GAnapatya Guru is recommended, but a Kaula is fit to be the Sathguru for all of
them. (Verses: 200,201)