I'm pretty sure the SubHarpoon has a booster
I'm not referring to the launch booster attached to the UGM-84 to launch it from 21" launch-capsule but seperate booster (The Mk-106 used on the UGM-109 when it went into service) attached to the 21" launch-capsule itself just like the VSM motor for the sub-launched SM-38 variant of the Exocet.
but I'm not sure which booster it is.
The R/UGM-84 used the A/B44G-2 or -3 solid-propellant rocket booster which had thrust of 12000 lb for 2.9 sec.