Is it a thing to be ashamed of if you have to start a song a few keys lower than in the original?

I feel guilty each time when I sing a song, I lower the key a little because I am naturally an alto, so I couldn't get my key to go up too high without hurting my voice. I would like to think that the song still sounds nice because it is in a key that is better suited for MY voice and MY abilities as a singer (and I am less likely to go off pitch when I sing inside my range), but I still can't help but feel like it's cheating to sing a song in a lower key than in the original song. Also, when people listen to a really good singer, they get the "goosebumps" and a chilly feeling. But I notice that often happens when there are high notes or a crescendo in a song, Is it still possible to bring out that chilly feeling in people if I sing the same song in a lower key?