The battery you linked is a 3.7 V LiPo with a 2-pin JST-PH connector, so it should be physically compatible and can be plugged in directly, no soldering required.
As noted on the product page for the Witty be sure to watch out for battery polarity - connecting non-Adafruit batteries with the wrong polarity can instantly destroy your Witty Pi and possibly the Raspberry Pi beneath.
I remember something a few years ago where a particular battery manufacturer had the wire swapped on the JST. If you just plugged it in, +ve and -ve were the wrong way around.
Suggest using a multimeter to verify the actual voltage on the JST pins and compare with what is needed by the Witty.
Cheers
Jim
Yes, the battery is compatible—Witty Pi supports 3.7 V LiPo batteries, and your battery fits the connector type exactly. No soldering required. It’s a simple plug-in connection.