You don't bankrupt a company by selling its shares.
You might make its share price lower, which in some cases might make it a tasty takeover target, but the price of a company's shares on the secondary market doesn't affect in any way shape or form the running of a business. You're only selling your ownership stake in the company to some other person.
With a well run company like Shell, if you divest shares and the price of the shares go down, it will be somewhat self correcting. The dividend yield will go up - the business's viability hasn't changed, so the dividend remains the same but you can buy into that with a lower share price - making the company more attractive to people who don't have a problem with owning shares in oil companies - thus stopping the share price from falling very far.
The only way you're actually going to hurt Shell is for everyone to stop buying their product. That isn't going to happen any time soon. It might happen over the long term, oil usage vs GDP has been falling for some time now. But selling Shell shares isn't going to put them out of business since it literally doesn't affect them.