The cellular modem is designed to interface with the SIM card, using the SIM card signal levels and protocols, primarily to provide cellular-phone features - i.e., ability to switch SIM cards for different users / accounts, secure identification, secure SMS storage, association of saved data to account, etc.
Because the SIM is a secure storage device, as far as I know, it is required by design, and cannot be replaced with any other storage type.
That said, it is possible to source surface-mount SIM devices (called MIM) for permanent installation instead of the 2FF or similar "cards" which require a socket. However, these are difficult to source in small quantities. But the short answer is, yes, you need one, and no, there is no way around it.
If this is a problem, then look into the other wireless services and technologies available in your area. Or consider, if you have several of these devices, could they just "RF link" to each other using any standard RF transceiver module and relay information to only one device with the desired capability? This may be far easier to implement than a creating a "cellphone from scratch."