This is frustrating however if you have access to A mode it can be accomplished.
Just set the wider aperture it still gives you decent image quality and focus and then move your ISO until you get your shutter speed of choice at that point lock AE. I would recommend a -0.7 to -1 exposure compensation
If the resulting image is useable you are good to go if not you need to take compromises. Typycally your camera will have a max ISO to go anyway
At surface in bright conditions even in program mode at ISO 100 I get regularly 1/250 with f/5.6 - f/8 in Egypt at the surface I am sure you can work it out