The same softirq can run on the other CPUs: you can use a per-CPU array (see the section called “Per-CPU Data”) for better performance. If you're going so far as to use a softirq, you probably care about scalable performance enough to justify the extra complexity.

You'll need to use spin_lock() and spin_unlock() for shared data.

You'll need to use spin_lock() and spin_unlock() for shared data, whether it be a timer, tasklet, different softirq or the same or another softirq: any of them could be running on a different CPU.