Hi.Is this a private share save plan or were the shares acquired through a Save As You Earn Scheme operated by your employer?
If the shares were acquired through a SAYE scheme, you have several options for mitigating tax which you can read about here. There is nothing to stop you transferring some or all of the shares to your wife before you sell them in order to get the benefit of a second CGT exemption of £10,900 and possibly the lower rate of CGT of 18%. If you split the holding on a 50:50 basis the cost for each of you and your wife of your respective holdings will be £8,750. The cost has to be divided proportionately.
I hope this helps but let me know if you have any further questions.