Speed shimmy on new hybrid

Just out of curiosity how much seat post have you got showing?

I was going to suggest tyre pressure as I had the same experience with a new bike from Evans, it got wobbly at around 50mph, turned out the tyres were way too low.

I experience the dreaded wobble every time I ride through a certain corner on a certain hill. I found the only way to stop it was to slow down.
One area I did discover had an impact on the wobble related to stem length in relation to the front axle. Imagine a plumline from the end of the stem, the line should sit behind the axle, but if you raise the back wheel to mimic going down an incline you'll see the plumb line move towards the axle. Once it goes beyond the axle you've got yourself an unstable situation as weights now in front of the axle. The longer the stem, steeper the incline the more likely the wobble scenario.
Might be worth a look.

Saddle to High? I played around with my saddle height and had it set about 20mm above where it is now the front felt light and on a couple of occasions at speed (around 30) the bike would violently shake got to the point i would avoid a certain hill because the bike would always do it. Dropped the saddle in stages and never had a problem since the bike.

Do the handlebars turn smoothly? If the headset has been done up too tight and the handlebars are not completely free turning, your handling will feel dreadful (and possibly quite scary). However, as DavidC points out, this will not cause wobble unless your physical inputs are overreacting to the fact that the steering is not turning quite as it should. I made the mistake of over-tightening the headset once when fitting a new stem. Won't do that again!

Very, very unlikely in a brand new bike, but the other experience I have had of poor steering is if the fork has a bent steerer tube. For me, it took a long time to identify the issue because the damage to the steerer tube was so slight. Was caused by a big crash, but the bent tube was not at all obvious - I could only be sure when I put a ruler up against it - but it made the bike very difficult to ride.

First, perhaps what you are experiencing is not shimmy/speed wobble. You describe it as "an unstable feeling", whereas wobble is the handlebars/front wheel shaking violently and the bike is out of your control — there is no uncertainty about when it happens. Speed wobble is very dangerous.

Most of what people believe to be causes/fixes for wobble and post online are not true (eg. headset too tight or too loose is popular). Any caster wheel can produce wobble, given the correct circumstances. The sum of you, your bike, how it is set up, the road surface, the speed, etc., produces the circumstances in which the feedback loop starts. Change one (not a stereotypical anal-rider change of millimeters/grams, but a meaningful, big change) and the loop will not start.

If wobble does start, clamp your knees on the top tube as far forward as is possible. Do not use the "unweight the saddle" method sometimes suggested as being an instant cure-all — it does not work.

It may be something as simple as a poorly fitted front tyre. Or wheel/tyre deflection due to the rider/weight combo that you mention. That's where I'd start looking...