I suggest you take up the trip to Haridwar and Rishikesh first. Train options from Delhi till Haridwar available. Go to Rishikesh via road. There is a special train running from Delhi to Katda - Vaishno Devi.
You should start journey from Maa Vaishno Devi, then Hrishikesh and Haridwar
Nd also Heli facility is avble if it's not pssble to trek till temple shrine
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Can trekking be completely avoided with this facility..?
Best time to visit these places is Feb March when it's not too cold over there Nd There are direct trains from Katra to Rishikesh
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Your plan just perfect .