Wobbly Tire Theory -- Is there an existing theory that fits the following description?
I don't know if this theory has any formal name, but of course you are correct in assuming that any mass redistribution on or in the planet will affect it's axis of rotation, causing a wobble. Small re-distributions are happening all the time with growing and melting ice, ocean currents sloshing water from one side of an ocean to another (as in the El Nino). Theoretically, a whale swimming across an ocean will create an axial wobble, albeit far too small to measure. Earth and sea tides, climate change, plate tectonics etc... The list goes on and on, with multiple processes each causing a slight tilt in the Earth's axis. This ranges from barely detectable sub-milimetre range to thousands of kilometers (over geological time - hundreds of millions of years).

In addition to the above random fluctuations there is also the 'Chandler wobble' which is a predictable cyclic wobble in the Earth's axis, of about 9 metres, over a period of 433 days. 

As for human impacts, until recently I would have said that they were puny compared to natural processes. However, recent research points to significant and growing change in the Earth's rate of spin due to human induced climate change. This could have interesting 'knock-on' effects upon the spin axis. The effect is absolutely miniscule, but as the Earth's spin slows, there is likely to be further de-coupling of spin rate between the Earths crust/mantle and core which could well be an additional component to the axial wobble.