ANSWER - I don’t think you would have a problem doing this at all. There are certain witches who in very specific circumstances do choose to place spell work on their writings with the intention of harming anybody who reads them but it is unlikely these would survive a passing. It’s also quite rare – most witches either live alone or with people they trust entirely - there is simply no reason for many witches to infuse their private writings with negative magics.
You can take some basic precautions – light a white light nearby, a quick smudging, a respectful word as you open the books to the effect that you are doing this to learn not to pry. May also be worth having a word with the friend about the kind of person her cousin was. A good character reference may make you feel more confident that the books are not infused with malicious intent. But like I say, very unlikely such intent would survive a passing, it would have to be magic totally disproportionate to something as simple as deterring strangers from reading her private notes.
That isn’t to say though that there may not be some danger involved in reading the writings of another witch. The primary issue that I would envisage would be that you would be swayed too heavily toward following the footsteps of the witch whose writing you were reading rather than carving out your own niche on your personal magical path. Think of it like a computer game – you might get to the end quicker with a walk through guide but you miss the experience, the knowledge and the sense of achievement involved in getting there on your own. You also may end up taking a very different road ahead than the one you would have taken if you had allowed the natural passing of time to guide and educate you.
There is often a tendency to revere the dead and take their words as absolute truth and there is a real danger that you may trust what you are reading above your own instincts. That would be detrimental to your own growth and development. If however you believe truly that you are capable of reading these books objectively – looking for ideas and inspiration but staying away from any temptation to follow/copy - then you may well find you have a very useful source of wisdom on your hands.
To be fair, I’d be a total hypocrite to tell you not to do it as given the same opportunity I know I would read those books like a shot.
Just as a postscript to this - in this specific situation the intentions of the deceased witch have not been made clear. Where specific wishes state that a witch wants her writings not read or destroyed on her passing my advice would have differed from that given in this particular situation.