A beam balance, some balloons, and a weight set
Since the alarm takes a few second to go off, we can use a risk free solution!
First, attach a balloon to a beam balance, so that the whole configuration is neutrally buoyant (you will probably want a tank of helium or hydrogen to adjust the balloon's size). Now, remove the artifact, put the beam balance on the pressure plate, and then place the artifact on one of the scales.
Now, you can place test masses on the other scale to determine the mass of the artifact. Note however that you must also attach more balloons to the balance, or the more weight will be exerted on the pressure plate. Therefore, before adding a test mass to the scale, blow up a balloon that neutralizes the buoyancy of the test mass. Note that since the pressure plate is slow to react, you do not need to put the test mass on the scale and attach the balloon to the balance at exactly the same time. Just remember that when removing a test mass, you must detach its balloon. I recommend using different colors for all the balloons to help you keep track of which balloon goes with which weight. This also adds variety.
Once you determine the mass of the artifact using the test masses, you can just dump the test masses onto the pressure plate and remove the balance (along with the balloons and the artifact). Additionally, you can use the test mass neutralizing balloons to neutralize the weight of the artifact. This is not technically necessary, but that way instead of carrying the artifact and scale home, you can just pull them home, which will be much easier on your arms.
If you do not want to abandon the test weights, you can bring a second scale so you can find another object with the same mass of the artifact.