I am not sure if you are trying to meter exposure, or tune white balance. If you are shooting on manual, then the meter is not going to do much for you, really. Under a standard illuminant with fixed exposure settings, you should be able to photograph any of your pieces of art at the same settings, and have all of them expose properly. With a digital camera, it is easy enough to use a little bit of trial and error to get the exposure you want (vs. the exposure the camera may tell you is correct, which is based on a set of immutable rules that do not always reflect reality as closely as they should.)

If you are trying to tune white balance and/or check the color accuracy of the photographs once they are imported into your computer, then you can do one of two things. First, you could stick with your gray card. Include the gray card in one shot, then take a second shot without the gray card. During post processing in a tool like Lightroom, you can use the white balance picker tool to select the gray card, and the rest if the picture will be adjusted accordingly. Simply copy the white balance (temperture on the blue/yellow-orange scale AND tint on the green/magenta scale) to the second shot to get a properly color corrected image without the gray card in the scene.

If you want to not only calibrate white balance, but also check color reproduction, you can use a color checker card (originally GretaMacbeth, however it is now owned by X-Rite). A standard color checker card has a set of 24 standardized, specifically formulated colors that have a specific base tone and color under a specific illuminant (usually D50, I believe). To archive artwork with maximum color reproduction accuracy, you would want to set up your illuminant to the same color temperature as that used for the color checker card, which is going to be much more of a natural, normal white than the standard tungsten type of lighting. (I would avoid illuminating your scene with flourescent light, as there are inherent problems with such lighting.) A daylight balanced bulb (which is what a D50, D55, or D65 bulb would be) can be expensive...however its light is more pure and better for color accurate color reproduction.

When doing color checking, you will not only want to adjust your white balance on an 18% gray card, but you will also want to compare the colors of the swatches in your photograph with that of the real color checker card. Make sure you correct white balance first. Any perceptually significant deviation in any individual color on the card in the photograph will be fairly easy to spot. If there are any significant deviations, you can either try to correct them with some fancy curve work in Photoshop (or Gimp), or find a way to illuminate your scene with a purer white (i.e. switch to a daylight balanced bulb from a standard tungsten bulb.)