We are transiting through Guangzhou. We have 4 days until our flight out of Guangzhou.

No, this is not possible because mainland China and Hong Kong have different immigration authorities. In other words, when you exit to Hong Kong, you are considered to have exited mainland China.

In reality, this is doable under another, but rather complicated arrangement. For example, your original flight ticket is:

London - Guangzhou - Singapore (just as a presentation)

You can buy a ferry ticket from Guangzhou (Nansha port) to Hong Kong and after 2 days in Hong Kong, you can return to Guangzhou, but this time it has to be done by a direct flight.

Like this, your itinerary would look like:

London - Guangzhou - Hong Kong
Hong Kong - Guangzhou - Singapore

In other words, you would be eligible for 144 or 24 hour visa free transit twice. Please, just have in mind that during the first stay in Guangzhou you should stay there for at least a minute longer than 24 hours before going to Hong Kong in order to be eligible for 144 hour visa free transit.