There are lots of challenges to testing a static system the way you describe.
First, you need something to fit over the static port (not too hard if it's a single fuselage port, slightly more difficult if it's two of them, and if it's on a mast like on some Piper aircraft you just lost a lot of "seal area" and made the task very difficult).
You can get around that with test kits by taking the static line(s) off & screwing the test kit directly to the plumbing, or by using a variety of adapters that come with the kits.
Second, you need to produce a known absolute pressure in the line and hold it for a given duration to check for leaks.
That's most of what those fancy boxes do - they bring the line to a given pressure altitude, and then you watch the altimeter and/or line pressure to see if it leaks air back into the system.
All that said, if you're willing to deal with a really rough test, you can still do this with a syringe and some medical tubing. This RV-12 builder shows you how:
- Attach a syringe to some surgical tubing.
- Put some air-tight tape over your other static port (if applicable)
- Put some modeling clay around the static port.
DON'T get it in the hole - make kind of a cup around the hole.
- Put the surgical tubing into the modeling clay and press the clay tight around the tube to seal the chamber over the static port.
- Pull on the syringe until you "climb" to a convenient altitude.
- Hold or lock the syringe in place and watch the altimeter to see how long it takes for air to leak into the system and lower your altitude.
This is nowhere near as precise as proper calibrated test equipment, but it should help you detect a gross leak in the static system.