I had a chicken pox vaccination because I don't want to have any marks on my skin from them.
この場合、次のような言い方ができますよ。
ーI had a chicken pox vaccination because I don't want to have any marks on my skin from them.
「皮膚に跡が残るのが嫌だから、水疱瘡の予防接種を受けた」
chicken pox で「水疱瘡」
to have marks on one's skin「皮膚に跡が残る」
ご参考まで!