I find this notion amusing because I think Hinduism is just opposite.
Yes, what you think is right.
So, no Hindu scriptures say that Hinduism is just a way of life.
But. having said that i need a more precise definition of- way of life vs religion.
If way of life means something like - not much restrictions, plenty of options to choose from, no clear cut instructions as regards what to do and what not to do, how to lead a righteous life as per Dharma and what to be shunned as unrighteous, etc then that's not true.
All scriptures like the Smritis, PurAnas and the Tantras are full of SadAchAra principles and Dharma-Adharama Nirupunam (determination of what's righteous and what's not).
What to be eaten, what not be eaten, how to eat, which mantras to chant before commencing the act of eating etc are also laid down quite elaborately in the aforementioned scriptures.
So, the answer to your currently poised question is No. But there's no way of proving that no.
Also, upon seeing one of your comments under the question, it seemed to me, that you are of the impression, that Vedas don't talk about righteous-unrighteous, moral-immoral at all. Then, that is not true.
I have collected few mantras from the Atharva Veda:
The path of truth should be followed:
rtasya panthAm anupashya sAdhu
O sAdhu, look (inside) and follow the path of truth.
One should always speak the truth and not falsehood; one should speak pleasantly:
Satyam vakshyAmi na anrtam
I will speak truth always, not falsehood.
Madhumatim vAcham udeyam
If you speak, speak only pleasantly.
Money should only be earned by legal means:
RamantAm punyA lakshmir, yAh pApih tA aninasham
The person enjoys who gets his money by honest means, the evil one who
gets his money by evil means is surely going to be destroyed.
Further mantras are there which can be produced to prove my point. So, DharmAdharma Nirupunam, SadAchAra principles are found in the Vedas too, but not as elaborately as they are found in some of the later-day scriptures.
NOTE- Whenever AV appears in my answer it denotes Atharva Veda.