Is this sentence correct? or rather, is there any way of improving this sentence (by possibly substituting in new words or even changing the sentence completely so that it still keeps its message)?
Does this sentence make sense “you can do it however way you think is best”?
No, that sentence would not be correct. A more correct construction would be:
"You can do it whichever way you think is best."
Removing the "-ever" and reordering the sentence may help demonstrate why this is the case.
"How way should I do it?" ✗
"Which way should I do it?" ✓