Now I don't have the time to remove all the skirting and refit it so I
was wondering if there was an alternative?

However, there is an additional advantage to removing the skirting, so you
should consider it. If you remove the skirting before sanding, it will be
much better to the edge, as you will be stopping 2cm beyond the end, rather
than a couple of mm before it, which will provide a nicer finish. You also
get to replace the skirting with new wood, so you don't have x years of high
gloss skank on it.

Christian.