I would really shy away from that solution and force the users to ensure they've input negative numbers. Consistency is always better! (makes any changes, should they be required, that much easier to implement)
Having said that, you could use custom formatting for optics and then change the values to negative via a formula when performing your calculations. Formatting like:
_(* (#,##0.00);_(* (#,##0.00);_($* "-"??_);_(@_)
and then the formula would be something like:
=IF(A1<0,A1,-A1) & the rest of your formula
Hope this helps out.