The problem is we don't know Exactly what the composition of the existing glue is... therefore .... it would be safer to get it all off... if you spray new stuff on it and it SOFTENS the old stuff... that might be a problem....
It is always safer to take it down to paint surface and be sure wax and silicone are removed.... ie, treat it just like you would a paint job...
Klix88 is the common cleaner right before painting to get everything including accidental touches by hands off...