Question: I have read some time ago that [z] is the voiced counterpart of [s], as [d]-[t], [g]-[k], [b]-[p] and [v]-[f]. For all pairs except the first, I was able to consciously perceive it by starting to pronounce the unvoiced consonant, adding voice and realizing that I am now doing a voiced consonant.

However, when I start to produce a S (AFAIK a hissing sound) and add voice, I don't get a Z, but rather a hissed Z. AFAIK Z is the same sound a flying insect (eg bee) does and has no hiss on it. Or is that another phone? Am I the only one who perceives this difference between a voiced S and Z? I don't know if I'm mispronouncing [s] or [z], somehow affected by my native language (Brazilian Portuguese) or by some regionalism.

Answer: 
Phonetically, the only distinction between a pure, unaltered IPA `[s]` and a pure, unaltered IPA `[z]` is voicing. However, most languages don't use pure, unaltered IPA `[s]` and `[z]`!

One phoneticist I know, for example, tends to pronounce English `/s/` as `[s͎]`: a "whistled" sibilant with a very distinctive, high-pitched "overtone". This makes his `/s/` very different from his `/z/`, in more ways than simple voicing.

I can't say for sure without a recording, but your `/s/` may be similar, or have some other feature setting it apart from `[s]`. If you want to make sure, I'd suggest finding some good phonetic recordings (the ones made by Ladefoged are especially famous) and comparing your `/s/` against them.
No, voice is not the only difference between /s/ and /z/. /s/ is fortis (forcefully articulated), while /z/ is lenis (weakly articulated). When I do your experiment, saying /s/ and adding voicing, without making other adjustments, I get exactly the result you report -- the /s/ made voiced doesn't sound anything like /z/ -- instead, it's an angry hornet sound.