Okay. So, on this system, in addition to the port with the three-way stopcock, there is another port at the transducer, correct? And this port also has a three-way stopcock and is usually capped off. This means you have two ports on the system: one closer to the patient and one at the transducer. To avoid confusion, I'll call one port the "transducer port" and the other one the "patient port."
Now, instead of capping off the port at the transducer, put a 10cc syringe on that port. Turn that stopcock off to the transducer, draw back on the syringe until the blood from the a-line goes PAST the "patient port." Draw back enough blood so that the tubing is filled with blood but doesn't quite reach the transducer port. The blood that goes past the patient port will be considered your "waste" blood. When you have your "waste", turn the transducer stopcock back to neutral. Now, attach your syringe for lab draws on the patient port and turn this stopcock also off to the transducer. This will allow the blood from the artery to enter the syringe. Once the syringe is filled, turn that stopcock back to neutral. Go back to the transducer stopcock, turn it off to the transducer again, flush the 10cc transducer syringe with the NS that you originally drew back, and then turn that stopcock to neutral again. Now, flush the line until the waste blood and the entire line is clear. Turn the patient port stopcock off to the patient, flush that little bit of blood that sits in the port where you drew the labs (have a CHUX or ABD under it to collect the fluid), turn it back to neutral and you're done.
Did I explain this okay? It's hard to explain without showing someone at the same time. But, at least with this system, you don't truly waste any blood, as whatever you don't use is returned to the patient without ever actually leaving the system. And, it's as closed as possible aside from the port that is open for lab you draw.