bswap eax will reverse the low 4 bytes of RAX, zeroing the top 4 bytes of RAX as part of writing the result to EAX. 32-bit operand-size is always available, you don't have to use 64-bit operand-size in 64-bit mode. Look at any compiler output for code using int and you'll see 32-bit registers being used. See also The advantages of using 32bit registers/instructions in x86-64
In fact bswap r32 is faster (1 uop, 1c latency) than bswap r64 (2 uops, 2c latency) on mainstream Intel (including even Ice Lake) https://uops.info/
The low 4 bytes forward and reverse are
00 66 6E 69 input
69 6E 66 00 32-bit bswap result
That gives the result you say you want, for this input. If you have some other requirement for larger inputs with non-zero high halves, say so. (If you have SSSE3, you can do an arbitrary byte shuffle on an XMM register; worth considering if a bswap r32 or bswap r64 isn't what you want.