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You can be honest without going into a whole lot of details.
It may not be appropriate for him to stay over your home. The two of you can look into renting a place. You may tell him that your dad has health issues and changes aggravate him. After all, you are talking about your geriatric dad. Irritability and anger can be evident in those with depression.
If this man is serious and dignified, he will understand a lady's concern and honesty.
Opted out because I was not sure the info was helping you and another expert can see it from another angle and offer more feedback.
Your expectation of him is quite reasonable. There is nothing wrong with him staying elsewhere. That way neither party gets stressed out.
You do not have to explain all of it to him. You have already indicated that it would be inconvenient. You also do not want their first interaction to be unpleasant. Just because your dad is struggling with issues, it does not mean that you have those issues yourself.