If I bring up Weavile with the "Assaulting Hunt" Ability after my opponent KO's my Active Pokemon, can I switch in 1 of their Benched Basic Pokemon to the Active Spot?
No, because Assaulting Hunt only works "during your turn"
Source: Paldea Evolved FAQ; TPCi Rules Team (2023-06-08)

Relevant cards

Note: All applicable cards may not be listed below.
SV2_134
SV2_134