Don't think that you need a perfect voice to be appreciated. SailorRon is an excellent example of someone whose performances are eagerly sought out by many people because he is well worth listening to despite not having the voice of an "Irish linnet".
If you really are unhappy with the sound of your singing then you could try songs that rely on their comedic element, or opt for poetry, or dialect poetry if that feels better, or try storytelling, which has its own challenges.

I used to visit a folk session where a new regular started coming and he was dreadful, and appologetic, but persistent. He was encouraged to keep trying and after a few months there was the start of a definate improvement which seemed to accelerate away. After about 18 months you wouldn't think twice about asking him to sing. Partly it was because he wanted to sing some particular songs that nobody else in the area was singing, so he couldn't join in the chorus!

I do know one person who cannot sing a scale, but can sing the notes of a chord. She doesn't seem able to sing a note an octave different from another one.