Is it preferable to ask the one to whom a good deed was done for the sake of Allah to conceal it, in order to avoid self-admiration and the loss of reward, and is self-admiration in such a case considered minor shirk or riya (showing off)?

There is no evidence that preferring to conceal good deeds over publicizing them is minor shirk (polytheism) or showing off (riyaa'). Rather, it is better for the recipient to keep the matter private, as a safeguard against people belittling them.

It is better for a Muslim to conceal their voluntary acts and charities, to preserve sincerity and avoid showing off, as stated in the Almighty's words: "If you disclose your charities, it is well; but if you conceal them and give them to the poor, it is better for you."

Among the seven whom Allah will shade on the Day of Resurrection is: "A man who gave in charity and concealed it, such that his left hand did not know what his right hand spent."

Therefore, concealing charity is better because it is further from showing off, unless there is a stronger benefit in disclosing it, such as inspiring others to emulate.