there's no right or wrong way to learn/utilize the scales, everybodies brian is wired differently (take Lali for instance)the important part is that you embark on the learning process.
After the 50th time of looking at the sheet to see the fingering for C major something magical will happen, you'll no longer need to look, you'll have memorized it. Once you memorized the ist one the rest come much easier.
If you think back you were probably asking yourself the same question about chords, do I have to memoize them or can i look off a sheet, I think you probably no the answer to that one by now! Good Luck!!