Why without having its mass? Most ways of determining MW involve taking a known mass of sample and doing measurements on it. Is it part of a mixture where you don't know the weight fraction of polymer, and can't extract it? The only way I know of to determine MW in that case is GPC with UV or IR detection (provided there are no interferences from other things in the mixture); then you need to calibrate the RT-logM curve using standards of known MW - which aren't always available for your polymer. GPC using viscosity or (I think) light scattering detection can give absolute MWs, but then you need to know the mass of your sample, which must be pure (nothing else to scatter light or contribute to viscosity). The other possibility may be end group analysis, e.g. by NMR, if you have distinct signals for the backbone and the end groups, you can determine Mn from the relative intensity. But that is difficult for high MW polymers because of the low concentration of end groups. I think "the hydroxyl number and the viscosity of the polymer" will only work if you know the sample mass and it's pure.