You have already asked once for a copy of your contract and your employer has been unresponsive. Sending you "the templates" is completely meaningless. You can reasonably assume they don't have it. If your employer does not have a copy of your contract then your copy prevails.
If the prevailing contract does not define a notice period then the law of the land takes effect. You should go ahead and give notice according to local law and custom.
If you give notice and then your employer suddenly discovers they have a copy of your contract after all, then you face two issues. One, you may have to serve out the contracted notice period, and two, the question of damages may arise.
If you had simply and carelessly attempted to violate the notice period clause of your contract, then your employer might rightly claim a breach of contract. Of course they can't show any actual losses but they can make you stay.
But if your employer withheld knowledge of the contract and thus kept the clause hidden, you have a cause for damages, since your current employer is tortuously interfering with your relationship with your new employer. They can cure these damages by letting you go.
So it's important to document your demand for a copy of your contract. Does your employer have a HR department? A legal department? In-house counsel? Who is responsible for your employer's legal obligations? Send a request to that person for a copy of your contract. Document this request, for example send it via email or registered mail. Failure to respond to your request demonstrates that your employer does not have a copy of your contract.
Since failure to respond takes time to establish, it's not reasonable to expect you to wait out that time before giving notice. Make your documented demand and then proceed on your own timetable.
As always, a random stranger on the internet cannot be your legal counsel, so you should lay this all out before a solicitor. Or someone at the labor board may be able to give you qualified advice.
