A good singer can decide whether to have vibrato in the voice or not, much early music is performed with no vibrato at all and many session singers on film scores etc use their voice like any instrumentalist, deciding whether or not to add the vibrato in. It is an aesthetic choice. It is also not necessary to vary the pitch, or bleat like a lamb, varying the pitch can lead to trilling and the hammer - like vibrato may sound great on Tina Turner but is quite strident and it isn't the only option. In a cappella music it is often better to have little or no vibrato - look up The swingle Singers on YouTube, especially the keyboard pieces like the fugues they do, amazing control.
Try singing the word 'yeah' on a fairly long note, then pulsing the breath on 'yeah, eh, eh eh' without changing the pitch and you'll get a feel for how gentle a natural sounding vibrato can sound and feel. A good singing teacher will help you get rid of excess tension which might make things head towards the hammer vibrato, and then help guide you to a natural sounding vibrato. Search online for someone qualified, say through the Estill organisiation http://www.estillvoice.com/
good luck!