CR1632 (3v) vs. Two AA's
A single 3.0v CR1632 Lithium coin battery has a capacity of about 125 mAh.  A single 1.5v AA Alkaline battery has a capacity if about 2500 mAh.  So you can replace a CR1632 by two Alkaline AA's (in series), and they will last twenty times longer.  A single non-rechargeable Lithium AA battery, like the Energizer Ultimate Lithium, has slightly more capacity at 3000 mAh.  They would last longer than Alkaline batteries in low-usage situations.

I can't see of any disadvantages other than the physical differences.

If you wanted to run it off a power supply, you want want to use 3.0v (not 3.3v).

You could use a LDO (low dropout) regulator to generate 3v from a 5v USB supply.  One suitable device would be the Microchip MCP1702 which will deliver 250 mA of current (plenty, considering the pendant is designed to run off a coin cell).  The regulator is available from Digi-Key.