Is there any online website that is offering it?
For instance Blockchain.com or Blockchain.info (same site) is offering a Bitcoin wallet.
I'm referring to very small payments where the risk of hacking etc. is so negligible.
When googling for I saw Centicoin.com says it will offer it, but it has been under construction for a long time.
As Pmalek says, Blockchain wallet does... but I don't see why you would want to do that even if the "risk of hacking is so negligible".
However, if you must, you can also use the
Counterparty Bitcoin web wallet. You still get to keep your private keys and you can use the "Pay Distribution" feature to make batch payments. You can even distribute tokens to the same addresses, and then distribute a percentage or share of Bitcoin to all these addresses for every distribution. You'll have to refer to Counterwallet documentation for that though.