HK -> Shenzen -> Singapore -> Shenzhen -> HK 144 hr visa qualification

You can definitely fly to Shenzhen from a country different than mainland China, then stay for up to 144 hours in the entire Guangdong province and then travel by train or ferry to Hong Kong. This is a travel on 144 hour visa free transit and no visa is needed.

The detail you will have to do before your departure toward Shenzhen is to buy your ferry or train ticket from Guangdong province to Hong Kong in advance as a proof that you will be in a real transit between X country before Shenzhen and Hong Kong. You will print out that ticket and have it in printed form at hand, ready to present to relevant authorities. Also, you should know that you will have to take exactly that ferry or train that you have bought in advance and presented at the time of your arrival in Shenzhen.

At the time being, Timatic still does not present the possibility to take a ferry from Hong Kong to Guangdong province and then to travel from Shenzhen to Guangzhou as possible although some documents show that such a possibility will be a reality in the near future.

To conclude, at the time being, only X country (Singapore in your case) - Shenzhen - Hong Kong is possible and the other way around not, although even that direction could become eligible very soon. In other words, taking a ferry or a train from Hong Kong to Shenzhen is not yet formally loaded into Timatic, so I do not recommend to take it at least until it becomes perfectly clear. As an alternative, I suggest you to rely on 5 days Shenzhen visa on arrival that you can obtain on the border crossing between Hong Kong and Shenzhen, preferably at Lo Wu (Luohu) border crossing. After your stay in Shenzhen, you can take a flight to Singapore. The price for a Shenzhen VOA is affordable - 130 CNY.