I would say that you should get the loan. You should be able to qualify for the best, or near the best, financing rates.
Your fiance probably won't qualify for the best rates. He has a substantially lower score and recent lates. Additionally, if he has current auto loan(s), it may make it a lot harder to qualify for an additional one.
The inquiries will hurt the score of whomever applies for financing. The good thing is that the inquiries, if financing is applied for during a 14 day period (I think it's 14 days), will only count as one in terms of scoring.