The one is to select the artwork and from the Swatches meny select "Add Selected Colors", this adds Global Swatches for the colours used in your selection, you can now globally edit the colour in your art by editing the swatch corresponding to the colour you wish to change. You can also "Merge Swatches" by first selecting the colour you want to have and then the swatch you want to replace and from the Swatches panel Menu choose Merge Swatches.
The second Alternative is to use the Recolour Artwork panel, In the advanced options you can limit to a colour Library and provided that you have a Pantone book you can limit to this colour book, which would make each swatch use the closest Pantone match. This is probably my preffered way to work as it also enables reducing number of colours. See: https://youtu.be/eYHGdB8nB-M for a great video on this.
A third option comes to mind. If you use the white arrow to select one colour, "select - same colour fill" and once all are selected choose your new swatch.