Is it permissible to present one's wife to a male doctor specializing in fertility for a procedure that assists in conception, knowing that there is no female specialist available, and would the husband be considered a 'dayyuth' if he were to do so?

The general rule is that it is impermissible for a woman to expose her awrah (private parts) to a non-mahram man. However, this is permissible out of necessity, such as for medical treatment. Allah Almighty says: (And He has detailed for you what He has forbidden you, except what you are compelled to [consume or do]). (Quran 6:119)

Treating infertility is permissible. The Fiqh Council has ruled that in-vitro fertilization (IVF) is permissible out of necessity, provided that the ovum is from the wife and the sperm is from the husband. The IVF procedure is considered a necessity that takes the place of dire necessity and requires exposure of the awrah.

Therefore, there is no objection to performing it due to the need to produce offspring, while noting that its results are often not guaranteed. It is preferable to postpone the procedure until a skilled female doctor is available, along with turning to Allah in supplication.