That stock will work but it won't be exactly appropriate. It is a straight grip stock intended for the 1903A3 and as such will need to have the barrel channel opened up to accept the rear sight base of your M1903, and then there will be a visible inlet left gaping right in front of the receiver ring where the handguard capture ring of a 1903A3 would fit. After all that is dealt with you would still have a heavy stock (they were "fatter" stocks than those for M1903) without the finger grooves in the fore end that a M1903 stock should have. Inletting on those wartime 1903A3 stocks was also sloppier than those on prewar '03's.
That said, in wartime they rebuilt boat loads of M1903's with whatever parts fell to hand. It was an expedient for getting as many functional rifles into the hands of those who needed them. So, it wouldn't be terribly wrong to put that stock on a pre-war M1903- but if you're going to all this expense and trouble why not use the correct stuff? It's no longer wartime and we aren't under threat of German/Japanese attack anymore.
I'll give the same advice I've given to a lot of other guys in the same boat you're in: if you don't have a copy of Bill Brophy's book on the 1903 Springfield, take a deep breath, grit your teeth, and buy a copy then digest it. It'll save you a lot of grief down the road, and make your appreciation of that iconic rifle all the deeper.