And how sure are you that the coins actually get sent and received in your already stored and tucked to safety wallets bearing in mind that lately some Bitcoin transactions don't get confirmed? I will like to know if there's another way of knowing this apart from the blockchain info.
If you're making use of a reputable service to buy your coins from, they will very likely include a decent enough fee that will grant you a sub 5 block confirmation. Thus far almost every withdrawal to my own cold wallets have resulted in sub 2 block confirmations. Concerning your other question -- if everything is stored in a safe, then there is not much to do other than to regularly check your address through various explorer sites. Is that a problem?