Answered by Ustadh Salman Younas
Question: Are products containing “lime extracted in vodka” and “rosemary, an anti-inflammatory and antiseptic, steeped in vodka” halal or haram?
Answer: wa `alaykum assalam
This would be permissible to use on the body. However, it would be better to avoid and find alternatives that do not contain such ingredients.
The ruling when it comes to alcoholic content in care products, such as the one you describe, is that they are permissible so long as they do not contain wine derived from grapes. As for non-wine alcohol, it is not considered ritually impure and so its use on the body is permitted, as affirmed by a number of senior scholars. [Taqi Usmani, Takmila Fath al-Mulhilm; Ahmad Zarqa, Fatawa]
For more details, I would ask you to read the following:
Can We Use Deodorants, Creams, and Perfumes That Contain Alcohol?
Checked & Approved by Shaykh Faraz Rabbani.