Yes, I do have support for RIP, but I'm affraid that in this case failover will be slow.

Do you have some other recommendation for faster failover?

1. Can I successfuly implement this with static routes?

2. Can I implement HSRP on L3 switches and connect router's interfaces to each L3 switch? On router I have HWIC-4ESW. I can create SVI on router and put two interfaces in access mode to same vlan. HSRP on L3 switches will enable failover betweeen switches.

Which solution should be best practice for this case?

"Yes, I do have support for RIP, but I'm affraid that in this case failover will be slow. "

Yes, RIP default's timers are can lead to slow convergence, but at least on Cisco equipment, timers can be tuned to dramatically reduce tables updates. (Got to be careful how fast you push the timers, though, since it can start to load up the device's CPU.)

"Can I successfuly implement this with static routes? "

Possibly if the only question is whether the WAN router is up, but if you need to know whether routes on the other side of the router are reachable, that's a problem unless you use something like SLA tied to routing.

"Can I implement HSRP on L3 switches and connect router's interfaces to each L3 switch?"

Perhaps. HSRP with interface tracking and static routes (#2) might be a viable solution if you only need to determine whether the next hop device is up and/or it's next hop link and you have no interest in reachable routes beyond the next hop device.