Warmly Welcoming Muslim Patients

Hey everyone, I work as a nurse in an emergency department and I'm a cultural Christian. A lot of my patients are Muslims from Somalia and Ethiopia, and I always try to treat everyone with kindness and respect. But I've noticed that my Muslim patients-some born here, some newer to the US-sometimes don't get the warmest reception, maybe because of language stuff and not knowing enough about things like prayer or fasting. I've been thinking about greeting them with "As-salamu alaykum" but I’m not sure if that’s okay coming from a non-Muslim. I don't want to be rude or anything. I already do little things like try to face them toward Mecca, find something for a prayer rug, remember Ramadan fasting, and ask female coworkers to help female patients. Would it be weird if I used that greeting? I just want to be welcoming, but I don't know if it's a universal thing or if I’m missing some context.