As others have said: most sight-singing classes don't care if your voice sounds well. It's all about reading, keeping rythm and holding pitch. It's not a voice lesson. You're not becoming an opera singer, you're developing a more intimate relation to written music.
For holding pitch, which I suspect is your main concern, a lot of it is about building confidence, more than voice technique.
First step for me was convincing myself I had the necessary range (being: an octave and a half, almost two, as almost everyone does). I had a lot of help from a tuner-app on my phone. Just make some vocal noise, in your low range, and in your high range, without straining yourself, and notice what notes you reach, you already will be amazed. Thing is: you almost certainly have the range to sing, you just need to practise to make it reliable. And this takes only time.
A second step was to realize that male singing (even when you have a deep voice) in the high range, sounds a bit, well, girlish. It took some time for me to realize that this is part of singing! You're not really singing if you are just using your voice in your normal speaking range. You have to get out of it. Just listen to the radio and realize: all those male singers are singing quite high, pop, rock, classical,... all of them.
Third, realize that to prevent your voice from breaking when going from your high region to the low and vice versa, you need to relax your singing muscles. To be able to relax, while singing relatively easy pieces (as you probably will in the beginning) is mostly a psychological issue. Don't worry, relax! It's ok.
Lastly, just do this, don't be ashamed, you won't be the only one in your class with no or little experience in singing. You're there to learn. Sticking your head out will be the fastests way for you to learn and will probably help the others too, by showing that you don't have to be perfect.