Using two independent switches is perfectly fine. You don't need a switch stack. With independent switches you could even have a better availability. A switch stack could fail as a complete system while two separate switches typically fail individually.
For your connections: If you use VLANs then you can*t put one vlan of one interface to the first switch and the other to the second switch. But you could do so with individual interfaces.
Another option is to connect one ASA to switch-1 and the second ASA to switch-2, you need an interconnection of the switches here. Or you could use redundant interfaces on both ASAs, one member connected to switch-1, the other to switch-2. The redundant interface gets subinterfaces for each outside connection. That is my preferred way to implement it.