Are you talking about MMIO registers (ex. $2002) or CPU registers (ex. A/X/Y)?
If the latter:
sta/stx/sty don't modify CPU registers.
If the former: any opcode that does a write operation to an absolute address, directly or indirectly, can affect an MMIO register. A
proper opcode list should contain a list of all of its addressing modes. Thusly, as an example,
inc/dec can indeed be used to write to an MMIO register.
HOWEVER, it's very important you understand how these opcodes work under the hood (at the silicon/transistor level), on a per-cycle level. These are often called T-states (timing states). A good reference
is here, though it contains some instructions for the 6510 CPU and I think some unofficial opcodes (blah, screw those). Scroll down to around line 891 for what I'm talking about.
inc/dec are what's called RMW instructions ("read-modify-write"), which means they behave in a way that is not immediately intuitive: they actually read from the destination address first, followed by writing the value read back to the same address (yes really!), followed by writing the new value desired to the address.
Why this is important: the read operation can cause oddities depending on if the MMIO register does something uniquely on a read, and the same goes for the fact that the MMIO register is written to twice. If there's a latch that increments or triggers based on read or write operation, you may find that the end result you desire is not quite what you get.
Here's an example:
inc $2000. The CPU would issue a read from $2000 (it's a write-only register so I'm not sure what value you'd get back here, maybe open bus? Others can verify), followed by writing the value it got to $2000, followed by writing the incremented value to $2000.
An even scarier example would be
inc $2007.
The rule of thumb is: if you aren't completely sure what the behaviour of the MMIO register is, don't use RMW instructions on them, stick with instructions which issue a single write and do not involve a read or issue two writes.