In a SIGILL handler, how can I skip the offending instruction?

It's very hacky and UNPORTABLE but:

void sighandler (int signo, siginfo_t si, void *data) {
    ucontext_t *uc = (ucontext_t *)data;

    int instruction_length = /* the length of the "instruction" to skip */

    uc->uc_mcontext.gregs[REG_RIP] += instruction_length;
}

install the sighandler like that:

struct sigaction sa, osa;
sa.sa_flags = SA_ONSTACK | SA_RESTART | SA_SIGINFO;
sa.sa_sigaction = sighandler;
sigaction(SIGILL, &sa, &osa);

That could work if you know how far to skip (and it's a Intel proc) :-)