AWG NEUTRAL 15A GFCI?
No. This setup will not work. 

You cannot add a loose neutral or hot wire to a cable like that.  

If the mini-split absolutely requires neutral, then your only play is to replace the entire cable with 10/3 or 12/3.

If you are madly in love with that GFCI recep and cost is No Object,  then replace the entire cable with 10/3 or 12/3. 

Otherwise you don't need or want that disconnect.  Get a simple one with no recep.  

Honestly you are probably better off keeping the fused disconnect you already have... and changing the breaker in the service entrance location to 20A.  When multiple devices provide overcurrent protection is in a chain like this, only one of them needs to be the correct value.  The others can be larger.  

So your existing 30A fused disconnect can continue in service if you simply change the panel breaker to 20A.  It no longer functions as overcurrent protection, simply as a disconnect.  But that's fine.