Will the presence of TFA be a problem? In many cases, it's common to simply use peptides as their TFA salt.
If TFA would be a problem, could you use the HCl salt? If so, simply dissolving the peptide in an excess of 1M HCl then removing the solvent should get rid of the TFA, leaving you with the HCl salt.
To get rid of all acids, I'd lean towards ion exchange - pass it through a short column of Amberlyst or Dowex resin, where the peptide should stick, wash the TFA out with a little water, then elute the peptide with aqueous ammonia. Removing the solvent (presumably by lyophilisation) should also get rid of the ammonia!
Finally, if you think a simple base wash is the way to go, just try it on a small amount to ensure that your peptide is actually soluble in DCM or similar - the fact that it's an amino acid (terminal COOH and lysine side chain) could make it insoluble.
My bad on that last part - you've got a free acid group in your molecule, so a base wash will simply deprotonate that, leading to a different salt, but one that's still probably water soluble (and certainly DCM insoluble)! Try the ion exchange, if the presence of a lysine salt is not tolerable.