Hobbes sorry to hear that you have lost a bit of confidence, but well done on "getting back on the horse" and getting ready to get out there again.
I'd agree with Friendly, there is nothing wrong with reaching out to contacts. And you are potentially solving a problem they/their contacts have, so try not to see it has hassling/bothering them even though it can feel like it!.
It could be worth looking at your contacts to check if you should segment them, are there particular people that warrant a separate/personalised message?
However, the beauty of a non-personal message is that by its nature there is no room for any "sorry we haven't spoken for a while" etc. So maybe that covers it. And personal messages might lead to "we should catch up for a coffee", which is probably not want you need; you need a new contract.
I did something similar when I left a horrible job before I started freelancing and I got a good few leads from it.
Maybe something like:
"I do hope you are well.
I am about to finish an enjoyable and interesting management consultancy contract with a xx client, where I have been looking at xx.
I am contacting you, as I now seeking new opportunities and I wondered if you could keep me in mind if you hear of anything if you or any of your contacts are looking for support.
The sort of business issues I can provide support on are:
My full LinkedIn profile is here - xxxx. My mobile is xxxx.
I do hope it was ok to contact you.*
Best wishes"
*I did try to add a sentence about offering to reciprocate, ie if they want you to keep them in mind re your contacts. But actually I think it is probably best to keep it simple and focused on the main message. You don't even need to add the sentence about ' Hope it is ok' but personally I would, I am sure if I was a -s weeping generalisation - man I wouldn't bother!
The worst that can happen is they'll say "don't contact me", but that is very unlikely and the likelihood is you'll pick up some work.
If people reach out to me, I always try to help.
HTH
Good luck.