What is an example of a secure sigma proof? I want to implement Threshold Elgamal as described in section 6.3.1 and in the decryption phase each party must broadcast a sigma proof to show that it actually has a valid secret share of the secret key. 

I read about Schnorr protocol as a solution for sigma proof but it is said to be insecure, in chapter 5 of the same lecture notes.

What secure sigma proof could I use ? 

It would be great if the sigma proof is non-interactive.
Sigma protocols as-is are secure only for honest verifiers. However, they can be easily compiled into full-blown zero knowledge protocols. If you don't want interaction, then the Fiat-Shamir transform suffices, with security in the random oracle model. With interaction, you can do the transform at little cost using commitments based on DDH. For more information on this, you can see this video. If you have Springer Online access, then you can also see this chapter. If you don't have access, then send me an email and I'll send you the chapter.