I'm not sure I'm actually following what you're trying to do?
Are you are asking 'I wonder if it would be a good idea to re-apply the heat compound to some chips in a computer that I am re-furbishing?'
if that's the question you are asking I would advise that in my 30+years of electronic maintenance on some very hi-end electronics we would routinely replace the heat compound on chips and transistors as and when we came to re-furbish electronic circuit boards. We regarded this as good practice.
You can either clean off the existing heat sink compound with a cotton bud and some alcohol etc and re-apply some new compound, or, latterly heat sink compound per se has gone bit out of fashion and it was quite usual to see newer equipment fitted with heat sink pads. These pads were usually cut from a grey blank sheet about 6 inches square so you could cut it to any size or shape. It's actually a very effective replacement, but, you should consider the thickness of the material to make sure it would not cause any mechanical problems in close fit mechanical finishes.
Available from RS components etc in the UK, not sure where you are from your signature. I hope this may help you in trying to achieve whatever it is you're trying to achieve. Whilst there is great deal of common sense in the if it ain't broke don't try to fix it scenario, I would, but then again I am very confident working with electronic components.
Edit. And I hope you're taking the usual anti-static precautions when dealing with circuit boards and components!