Some shells like zsh, bash or mksh automatically set the $COLUMNS variable to the width of the terminal, so you don't need to invoke stty here.
My implementationAll the implementations of ps queriesI tried that support that non-standard (BSD-type) syntax query the terminal width by itselfthemselves. I'm surprised yours doesn't. I expect it will look at the content of the COLUMNS environment variable though.
So you could do:
export COLUMNS; ps aux
If not,
ps aux | cut -c"1-$COLUMNS"
You can also tell your terminal not to wrap lines:
tput rmam
ps aux