Remapping without omap?

[Acumane]

Say I've remapped hjkl to ijkl (to be like wasd or arrow keys) and let h now enter insert mode:

noremap i gk
noremap j h
noremap k gj
noremap h i

I'm not using map or binding to, say, <Up> in the above snippet because they simply wouldn't work (please, prove this wrong!).

Given the circumstances, how can I get motions working without omap?
e.g. dhw... or even diw!

[userrand]

I did not test the following but maybe code each case (d, c, y, etc) individually like nmap yhw yiw