Any concern which you should have while doing something you believe to be righteous, would be that of whether it is proven by the way of prophet Muhammad s.a.w.w and his companions or His suggestions, OR is it any biddah?
Salat ut Tasbeeh is asked to be prayed in a daif hadees,so at least it is not Biddah..
So whoever does righteous deeds while he is a believer - no denial will there be for his effort, and indeed We, of it, are recorders.(21:94)
Following daif hadees for doing something righteous is NOT harmful.BUT taking any daif hadees to drive any Islamic law,or taking any daif hadees to show it as an evidence against Prophet Muhammad s.a.w.w is WRONG.