Is it safe to splice these cords with tape instead of a terminal?
No, I would not do that. 


First the one cord has a ground wire apparently not being picked up by the second cord.
They both should have the ground wire. 
Secondly it is not a safe procedure to splice a 120 VAC line without
it being protected in an approved box.
Third the splice should be made with an approved connector, such as a wire nut or crimp.


The best way would be to replace the entire cord with one continuous wire.