As a follow-up, here's the applicable paragraph from the Ameri-King manual. This makes it pretty clear - only the Ameri-King part may be used.
2.5.1 ELT MAIN UNIT BATTERY INSTALLATION AND REPLACEMENT
The Ameri-King Corp. Model AK-451 ELT is designed to use only with Ameri-King lithium battery packages which have been tested per TSOC126 and TSO-C142 requirements.
The use of any other battery will void any warranties of the ELT by Ameri-King Corp. The ELT does not meet the requirements of TSO-C126, TSO -C142, and TSO-C91a or FAR 91.52 if used with any other type of battery.
Additionally, this list shows the components which are required in order to maintain TSO approval of the device:
DOCUMENT NO.: IM-451 Rev. 4, Volume 1 of 2
APPLICABILITY
AK-451-(AF)(AP)(S): Emergency Locator Transmitter ELT,
406/121.5/243.0 MHz with GPS/NAV Position.
AK-451-PLB: Personal Locator Beacon PLB, 406/121.5/243 MHz
with external GPS/NAV Position.
451017-1B: Antenna, Whip type, General Aviation aircraft, 250 knots.
451017-2A: Antenna, Rod type, Business Jet aircraft, 350 knots.
451017-3A: Antenna, Blade type, Transport, 1.0 mach.
451017-4S: Antenna, Whip Portable type, 250 knots.
4500010-1: Battery Package, Lithium, LiMnO2, 90 Hrs Lasting.
4500010-2: Battery Package, Lithium, LiSO2, 87 Hrs Lasting.
4500010-3: Battery Package, Lithium, LiMnO2, 92 Hrs Lasting.