No need to doing some complicated trade like that mate, You are not only paying fee for withdraw but also paying trading fee (0.1%), The best way to do it's converting small balance on your main account to BNB and you can find this feature on binance wallet section, after that you trade it to BTC/BCH as you said you only hold that and then you can withdraw to your ledger, Beside that maybe you considering alts like LTC or BNB, It's costing small withdraw fee rather than Bitcoin or BCH.
but he needs to consider also that there's min trading amount of 10USD in binance. so if you are trading an equivalent amount of less than 10, i don't think it will go thru. so another option you can do is send those small amounts to another exchange that can accept small amount and trade it. he may not get the target amount that he wants but at least get something from it. make sure to check the min deposit/withdrawal of the exchange as well as the min trading amount.