If you have a terminal alkyne, you can shake it with the solution of CuCl in conc. NH3. Alkynes forms insoluble Cu salts with this reagent; these salts for short alkynes are explosive and quite sensitive, so never get them in dry form and/or in large amounts. On treatment with acid, they give back the alkyne. For internal alkynes the separation seems to be difficult, the only possible way is chromatography on silica impregnated with AgNO3, but it works only if you are lucky and is not that easy to perform.
I would prepare the solution of CuCl (about 3 eq to alkyne, conc. ca. 0.5-0.7M) in ca. 10% ammonia and stir the mixture of the alkyne and allene with this solution for 1-2 h. All that should be done under inert gas. The alkyne should form a red precipitate of the copper salt that has to be filtered off, the allene remains as an immiscible layer. To make searation easier, you can add pentane in the end, to increase the volume of the organic layer. Naturally, such process may work if you have no polar groups such as amine or carboxylate in your alkyne/allene.