What is the best and most effective way to give charity on behalf of the deceased with a small amount of money, and what is the reward for giving charity on their behalf, bearing in mind the desire not to inform anyone?

You may give charity on behalf of your uncle, and Allah will reward you for it. The reward of the charity will reach him as soon as you intend to dedicate the reward to him. Ibn Qudamah said: "Any act of worship performed, and its reward dedicated to a deceased Muslim, will benefit him – Allah willing. As for supplication (du'a), seeking forgiveness (istighfar), charity (sadaqah), and performing obligatory duties, I do not know of any disagreement concerning this." Charity given on behalf of the deceased reaches them, and the one giving the charity is also rewarded. It is best for one who gives supererogatory charity to intend it for all believing men and women, because it reaches them, and nothing is diminished from his reward.