You do not need DHCP snooping or DAI running on the 3750 core switch in order use those features on the 2960 access switches.
On the 2960s just enable DHCP snooping and DAI globally for the needed VLANs and then trust the trunk ports for both snooping and DAI. The commands will probably look something like this:
! Global commands on the 2960s
ip dhcp snooping
ip dhcp snooping vlan 1-4094
ip arp inspection vlan 1-4094
! Trunk Port on the 2960
ip dhcp snooping trust
ip arp inspection trust
Note that if you have VLANs with statically instead of DHCP assigned IPs, you will need to exclude them from the VLAN lists, trust the ports with static assigned IPs (not preferred if they really aren't trusted ports), or exclude the vlan from DHCP snooping and use ARP ACLs for that VLAN for DAI.
Also, if this is a network already in production make sure the DHCP snooping database has any existing leases already collected, before implementing the DAI commands otherwise some legitimate ARP requests will be blocked (or configure everything during a service window that allows re-triggering DHCP lease requests for all effected clients).
Cisco documentation for DAI is here