Are there any GA trainer aircraft without toe brakes?
There are still many Ercoupes in the fleet that don't even have rudder pedals, never mind toe-brakes on the rudder pedals.
You may also want to consider arranging for a more commonly-available trainer (e.g. Cessna 152, Piper Tomahawk, Diamond DA20, etc.) to be equipped with hand-controls for braking. This is done for individuals who have any number of reasons that they can't operate the rudder pedals with their feet, such as paraplegia, deformity, etc.
See e.g. https://www.freedomintheair.org/hand-controls/, https://www.newmobility.com/2019/01/pilots-planes-hand-controls/, https://www.wired.com/2009/08/hand-control-airplanes/, https://abilitymagazine.com/hand-controls-for-flying/, etc.