send to online wallet ie spend bitcoin from cold paper wallet ,without losing the remainder
Client normally means the wallet 

You don't need to give money to someone to make you a wallet. There are many free wallets like electrum , greenwallet, coinomi which create a address for you and also make you the owner of your private keys

You also don't need to send the money from your paper wallet . If you are able to destroy you paper wallet safely , you can sweep the bitcoin from your paper wallet to coinomi wallet .

No need to make a new private key every time .