"Safe" is the word that needs a condition attached. The guidance does not say yes or no across the board. It says yes with exclusions, and the exclusions are the part to read.
The answer depends on three conditions
NIDDK says to have a foot doctor trim your toenails if you cannot see, feel, or reach your feet, if your toenails are thick or yellowed, or if your nails curve and grow into the skin. If none of those describe you, the same guidance does not tell you to hand the job over. If any one of them does, the clause is plain: it is the foot doctor's job.
How to cut, when you do it yourself
The American Diabetes Association puts the technique and its reason in one sentence: "Be sure to trim toenails straight across—cutting into the corners of nail can cause ingrown toenails."
For the full pages, the American Diabetes Association has foot care tips, and the MedlinePlus Medical Encyclopedia has a page on taking care of your feet with diabetes.
What to confirm, and with whom
Tell your doctor or podiatrist whether any of the three conditions apply to you. Check all three, not only the first. Around Itasca, a foot exam is the natural place to settle it, and your care team can say which category you fall into.
Salon pedicures sit under the same guidance. NIDDK adds that if you want a pedicure at a salon, you should bring your own nail tools to prevent getting an infection.
The clause readers tend to skip
"Thick or yellowed" is the condition that gets overlooked. It is a description of the nail, not of your vision or reach, so a person who sees and reaches well can still fall under it.