7.4v battery instead of 7.2

Voltages

The page above discusses your situation, but the short story is that your battery is made up of older technology lithium ion batteries and the newer technology batteries have a slightly higher voltage rating. Yours is made up of two cells rated at 3.6V each, while the newer 7.4V batteries have two 3.7V cells.

If you do the math, the difference between 7.2V and 7.4V is about 3%. That's well within the 5 or 10% voltage tolerance rating for most electronic components. In addition, variations in voltage levels are always to be expected on any electronic device that uses a battery.

According to the Adafruit web page cited above, it's okay to use your old 3.6V (7.2V) charger with the newer 3.7V (7.4V) batteries; just don't try to use a 3.7V charger with the older 3.6V cells.

The short story here is that IMHO the voltage difference shouldn't be enough to cause problems with your Pill. If it was mine, I'd go for it, but you will definitely have to make your own decision on this.

A more serious concern is mismatching battery chemistry and battery controller. The controllers configured for a specific chemistry. If you connect it to a different chemistry, you run the risk of problems, primarily with charging. BTW, the 3.6 V is the nominal voltage. The actual voltage varies from 4.1 V to about 3 V as the battery discharges. If you install 3.7 V cells, they are unlikely to charge to 3.7 V, since the controller is configured for a 3.6 V cell. As noted above, this means it probably safe to charge these cells.

Taper current is also likely to be a mismatch. Some safety feature may also be mismatched. Not an ideal situation. As a general rule, cavalier attitudes toward lithium cells can end in tears. Lithium cells are inherently unsafe.

Common chemistries are lithium cobalt (3.6 V) and lithium polymer (3.7 V).

I would strive to match the chemistry. Drop-in battery packs with the correct chemistry are available (I found one on ebay, but I'm sure they're available elsewhere).