adverb
as you see fit; suitably; properly
Used when leaving a matter to someone's discretion or asking them to handle something appropriately. Often appears in polite requests or instructions.
あとはよしなにお願いします。
Please handle the rest as you see fit.
詳細はよしなに取り計らってください。
Please make the arrangements for the details as you think best.
うまく means 'skillfully' or 'well' and focuses on the manner of doing, whereas よしなに emphasizes leaving the decision to someone.
Derived from the classical adjective よし (good) + なに (adverbial particle). The exact historical development is uncertain, but it has been used since at least the Edo period to mean 'in a good way' or 'as you think best'.