Very easily

Load the *.cue file, select all tracks, rightclick on them and point to the Utils submenu. There you will find „Write APL link files”.
After that, you will get small .apl files in the same folder as your big .ape.
Now you need .cue just for burning

When you want to listen, just drag those .apl files to foobar and that's it.
The advantage is that you can tag those .apl files (with APEv2 tags) so that you can have much more info than what is stored in a .cue file.
It also works for .flac and .tak images, I'm playing my own collection that way.
Cheers