Conductivity of molten or aqueous salts
You cannot determine individual ion's molar conductivity at 1 M. The ions are not independent enough. Kohlrausch's law of independent migration of ions does not apply, it only applies at a fictitious concentration of 0 M NaCl! This value is found mathematically by extrapolation to zero concentration

Is there any way to compute the molar conductivity of an ion without
any experiments?

Yes, if you look up the tables of molar conductivities at infinite dilution, then you can determine molar conductivities of individual ions.