There are several Cisco devices on my network which I can find with
nmap but I have no idea what the type (e.g. switches, routers) or specific model is. Is there some way to find this out without physical access or having a login to any of these?
ICMP cannot be used to extract information like that.
Without a login you maybe have one option:
Hope that SNMP is enabled and using a known community string like "public". SNMP will at least reveal an OID you can tie back to a model number using SNMPwalk. Plenty of tutorials out there on how to do this.