You are in a difficult situation.
Leaving aside for a moment the choice of charge (i.e. Common Assault or something more serious) if the case goes ahead and a trial is held you will simply be a witness for the prosecution. You have no right to legal representation in those proceedings and the advocate who prosecutes the offence will not, strictly speaking be “on your side”. You will be there solely as a witness to help secure a conviction. You will certainly not be able to consult with him prior to the trial nor will he be able to offer you any help or advice other than to acquaint you with the trial process to be followed in the court. So from this aspect there is absolutely no point in you engaging your own solicitor.
Now, the choice of charge. From your description the charge of Common Assault does seem unduly lenient. This document explains the criteria for the various charges. See the section “Common Assault vs ABH”:
http://www.cps.gov.uk/legal/l_to_o/offences_against_the_person/#common_assault
Defendants are often charged with the more serious offence and that decision may be reviewed and a lesser charge substituted (especially in return for a guaranteed guilty plea). But there is no provision to review the choice of charge upwards. I should think it can be easily argued that an injury to your head where the medics suspected a fractured skull can be classed as “serious” (even if the eventual diagnosis revealed no fracture). But you are where you are and the lesser charge has been preferred.
Victims have the right to challenge a CPS charging decision when they decide not to prosecute at all:
http://www.cps.gov.uk/victims_witnesses/victims_right_to_review/
However, I may be wrong but as far as I know, they have no right to challenge the choice of charge. So from this aspect as well, I’m not sure there is any mileage in engaging your own solicitor.