Audacity is actually a very slim program, compared to most other DAWs. I see no reason why you shouldn't use it for this application, in fact it seems quite a good fit. (Apart from the possibility that you might end up needing features not contained in it!)
Of course, if all you want is to replay a recorded audio file at more than 0 dB volume (i.e. more than 100%), then many off-the-shelf audio players will also do the trick – VLC would definitely work; banshee, audacious, good old winamp should also be able to get the job done. However, I wouldn't recommend that – you may end up using the player also for some fully-mastered music file, which is then loud way into distortion.
A better approach might be to normalise all the files, i.e. to gain up each file (without playing it) exactly as much as possible without distortion. I would do that with ffmpeg, but there are plenty of (probably simpler) tools around that do the same thing.
The real question is why these recordings are so quiet in the first place. If you can simply boost them significantly without introducing distortion, it means the gain was not set up correctly while recording. Get a better mic/preamp/recorder, if yours isn't able to do that. Boosting the signal after recording always means you're also boosting the noise.
Quite possibly though, you can't actually boost without distortion. Note that a dry vocal recording has a really high dynamic range, which means there are some rather useless loud sounds (e.g. “plop” plosives), but the parts you need for understanding are way quieter. In this case, you need a dynamic compressor (and probably an EQ too) to get the effective volume to useful levels. Audacity can offer both, so again I'd recommend using that.
