ft
Yes I fully agree with your calculation I made it about 22.6 KT along the heading vector and about 44 KT at right angles.
If you draw the vector diagram or use a CRP then you will see it pictorially.
The easy practical way is to use 'effective' TAS i.e.
TAS * cos Drift
But as you say it all depends on the definition of component.
Obviousy for performance runway calculations the reference is track which will be the runway centreline.