Fluctuating resistance in digital pot

I only have on hand 1uf and 10nf. I don't believe the large cap will harm anything (correct?), but will it be too large?

As long as that 10nF is a ceramic one then it should be fine. If it is any other type it will not. This is because ceramic ones have a low inductance and so handle higher frequencies.

I'm confused by how you are using analog in to drive serial clock and serial data lines to the device.

Because those are the pins used for the I2C bus.