I don't think clipboard can be set to anything other than unnamed or unnamedplus. Because, clipboard was introduced for associating vim's register with operating system's clipboard. But I'm not sure. Maybe someone can help me out.
My suggestion would be to use a simple mapping:
nnoremap d "_d
and when you don't need it anymore just do
unmap d
This should get you started for now. I'll try and come up with a vimscript function to toggle the situation before you become bored with this solution. Afterwards I'll edit this answer.
Edit: I came up with this hideous function. I don't know if it should be used or if it will hamper any regular use cases. But it works for now. Maybe someone will help me out. Here it is:
nnoremap <silent> <leader>tb :call ToggleBlackHole()<cr>
function! ToggleBlackHole() abort
if maparg("d", "n") ==# ''
nnoremap d "_d
else
unmap d
endif
endfunction
So, OP should be able to use <leader>tb
to toggle blackhole register and unnamed register for deleting.