This is where I need advise, so can minimize exposures. Read your column and know you are sympathetic to love and marriage. If you become pregnant by this man, he has the right to claim paternity at any time. And it will be his biologically, so you won't have any way to prevent this. There is no guaranteed quick way to become pregnant.
Some women become pregnant immediately upon trying, others take months, even years.
Unless he is ejaculating into a cup and passing you his semen, this means you have to be having sex with him several times a month until you conceive, which could take months to a year. It's hard to avoid an increasing attachment under those circumstances, especially since you already like this man. It's not fair to your husband to leave him out of the process of your becoming pregnant. Wanting to avoid passing on a genetic disease is a valid reason to seek insemination, and he should understand. By including him in the process, and having a completely anonymous, clean, donor, he can feel that this child is his as well as yours.