Is it possible to denote "any single alphabet symbol" in an FSA state diagram?
The formal representation of an automaton is the tuple giving its state set, alphabet, transition function, start state and set of accepting states. The diagram is not a formal representation: it's just an informal way of showing what the automaton does.

As such, you can label the arrows however you want, as long as it's clear what each label means. If you think a label might be unclear, you can always add a caption to your diagram that explains what it would mean.

"." is a poor label, since it's too easy to miss. "*" is a confusing label since, in regular expressions, "*" means "any number of times", not "any symbol". Since it's quite common to see arrows in automata labelled, e.g., "$0,1$", I'd probably label the arrow "$\sigma_1, \dots, \sigma_k$" and note in the caption that $\Sigma = \{\sigma_1, \dots, \sigma_k\}$. Or you could just label the arrow "$\Sigma$".