It will not be possible to duplicate any Musk fragrance using only Essential Oils, as the basis of the fragrance will be one or more synthetic materials called Polycyclic and Macrocyclic Musks. Even if you were prepared to use synthetics as well as naturals (and there really isn't any reason not to) it would be extremely difficult to duplicate this fragrance. If you really want this it would be better to try and find someone who still sells it.
OP, is this what you are looking for?
I have to admit that i have never smelled the fragrance you are after but I am guessing that it was based on synthetic musks. Ambrette seed oil does have a musky note but it isn't the same. It's also quite expensive, but have a go with it if you want.
By the way I just Googled "Coty Wild Musk" and found several different sites offering it for sale. But I'm sure you have already done that.
OP, another search found this link, which has the oil in stock:
However I do not know if this site is legit. Please shop very carefully!
I'm afraid I don't know this particular fragrance either but there are a great many synthetic musks and they all have different characteristics and are nearly always used in blends. I agree Ethylene brassylate is a good candidate and so too is Ambrettolide. My guess is that you'd be well advised to try some Musk Ketone though as it is still available though now hardly used in commercial fragrance, it was once very popular. I would also suggest you want some muscenone (not an easy one to buy in small amounts) and something like helvetolide or tonalid to give the top-note effect.
For $1000 you could almost pay for a perfumer to recreate it from an analysis if you have some of the old oil still to work from and choose a perfumer who is willing to ignore modern IFRA standards.
I have some original Coty Wild Musk and will smell it for you......
There is a very clean smell about this musk that has a naughty after kick. This is a nice girl with a wicked side to her. It has an initial clean white musk opening. There is a very powdery, slightly spicy quality to it. There is a floral note but very slight and on the violet leaf side of flowers. I'm getting a tagetes note too, quite raw and insistent. I'm thinking you will definitely need a synthetic musk to achieve this. I haven't got time today but I will smell the ones I have for you to compare later when I have a moment. Nudge me if I forget to. This could be quite fun to play with as a perfumers challenge.
A vanilla/benzoin note appearing softly now.