I want to print a number into log or to a terminal using write (or any async-safe function) inside a signal handler. I would prefer not to use buffered I/O.
If you really insist on doing the printing from a signal handler, you basically have 2 options:
Block the signal except in a dedicated thread you create for handling the signal. This special thread can simply perform for (;;) pause(); and since pause is async-signal-safe, the signal handler is allowed to use any functions it wants; it's not restricted to only async-signal-safe functions. On the other hand, it does have to access shared resources in a thread-safe way, since you're now dealing with threads.
Write your own code for converting integers to decimal strings. It's just a simple loop of using %10 and /10 to peel off the last digit and storing them to a short array.
However, I would highly recommend getting this operation out of the signal handler, using the self-pipe trick or similar.