Quite a lot of us are generalists in H&S, and if at the start of your career in H&S I suspect that is where you will be and may even stay. Therefore, in your opening post you ask us to give you a complete set of safe working procedures from process start to process end. However, the best way of learning is to do this for yourself, or at least review what you currently have, the same as we would have to.
The process of making syringes, starts with raw material being delivered to the company, and ends with loading up and shipping out the finished product. However, this can be broken down into its various stages, even elements of a production line. Pick one of them and go look at what is done, talk to operatives if you can. Look to see where the hazards are and what controls are in place and if there is a significant risk remaining. Is there a better way to do it? You must already be familiar with Risk Assessment, so go do it, it is the best way of learning, and you may spot something others have not. Once you have reviewed one area, move on to the next. The controls as decided by your assessment will form safe working procedures for operatives and management.
If any of us had what you are looking for and we supplied you with it, you read it, but you would not learn but just accept it.
This site is good for more specific issues as there are some helpful people. So, if there is an element of your production that you are concerned is not controlled as well as could be then ask on here about the specific task, giving detail of what happens and what your concern is and current controls. People will generally try and help, or at least give you food for thought. If nothing else you may get someone offer to review your Risk assessment.
I admit I normally hate it when people respond to others with, go do a risk assessment, which is obviously what they are trying to do normally, but in this instance, I think it will help you. Once you have assessed your entire production facility one part at a time then you could go to another factory making something else and do it again, and again.
It is no go me saying that if people handle the finished syringe there is a risk of a needle stick injury, so puncture resistant gloves would be needed as that will be obvious to you.
Not sure if this helps at all but good luck with your development.
Chris