How to issue the SLEEP command in Attiny
The asm instruction allows the entering of assembly directly; in this case, the AVR has an instruction explicitly for putting the microcontroller to sleep. You can't do this with a register - you have to do it by emitting the relevant assembly instruction.

There's no need to do this yourself, however - sleep.h is not a library, but a header file that's part of avr-libc, and including it and using it will incur no more overhead than doing it yourself; relevant parts will be inlined by the compiler, and any unused parts of the header file will not end up in the compiled result.