The field-angular dependence of Co-NMR spin-lattice relaxation rate 1/T1 has been measured for a 10% Co-doped single crystal of URhGe. The experiment revealed that spin fluctuations in ferromagnetic (FM) state of URhGe are robust against magnetic field below about 4 T, applied along any direction in the bc crystal plane. This is in clear contrast with the sister compound UCoGe, in which FM spin fluctuations are rapidly suppressed by a tiny applied field along the c axis. We show that such a difference in the character of the spin fluctuations is reflected in their two distinct phase diagrams for the upper critical field Hc2, providing further support to the mechanism of superconductivity mediated by spin fluctuations in these materials.