The dynamics of a 1D domain wall (DW) in magnetic wires patterned in 2D ultrathin Co films is studied as a function of the wire width w0. The DW velocity v(H) is hugely reduced when w0 is decreased, and its field dependence is consistent with a creep process with a critical exponent micro=1/4. The effective critical field scales as (1/w0). Measurements of v(H) in wires with controlled artificial defects show that this arises from the edge roughness introduced by patterning. We show that the creep law can be renormalized by introducing a topologically induced critical field proportional to (1/w0).