I would suggest going for simple text links - clean, clear, and concise understanding without users going through an extended dialogue.
Users should understand the system an apply existing metal models, one should understand icon functionality without thinking twice + avoid confusion at all costs.
I would suggest not to use 'X' icon for delete, this is very confusing and will break user expectations. The universal call to action for 'X' is close and should not be used for another function.
Trash can icon is a great choice however if you are compromising design, detail and size - then avoid using and stick with Simple text : )