Ligatures are not what you need. What you are doing is creating a cursive font, for which you need to use Contextual Alternates.
For this, you need to create two or more versions of some letters and use an OpenType feature to substitute the appropriate glyph dependent on the context. This alternate glyphs do not need any Unicode mapping, but they need to be named appropriately.
The linked thread above is a bit old, but I don’t think it is out-of-date yet.