How can I properly delete project 'skills'?

Hi, I’m using WP4 and have created 20 projects and display them via a page using the theme portfolio template. Historically, I have created a number of project ‘skills’ for portfolio filtering and have variously assigned and deleted these during development. Unfortunately, now that I require just 4 skills, even when I delete the surplus ones, I cannot effectively assign the 4 I have left.
At present, it seems that the CMS is ‘remembering’ some of the previously deleted skills and not allowing me to select (within the relevant project), any of the 4 I reduce the skills list to.
Is there a method by which I can completely remove all previously created skills, then recreate (they’ll need to be the same names as some I had created previously, though), a definitive set that I will be able to use?
Thanks and kind regards, MonkieWP