If you truly cannot do the work, of course you must tell the professor.
However, if you can do the work but it simply is harder (and takes longer) than you wish, then allow me to suggest another alternative.
Learn to read cursive fluently.
By doing so, you will cure this immediate problem and will have gained a potentially valuable (indeed, potentially lifesaving) skill for the future. A worker who can handle anything is intrinsically more desirable than one who can do only a portion of the work.
Perhaps more importantly, handwritten work often is a marker of reduced socioeconomic position, and it is socially responsible to be able to treat such students equitably compared with those who can afford computers and printers (and tutors and proofreaders). Homeless students, for example, may be unfairly disadvantaged scholastically, receiving lower scores for the same quality of work simply because it's more trouble to deal with handwritten work. This is a real thing, and you can help to make it better.
Fortunately, mastering this type of reading skill is not difficult and does not take vary long. Neuroplasticity is a wonderful thing: adult humans can grow new neuronal connections permitting them to recognize a new encoding of an alphabet (e.g., Morse code, mirror-writing, or cursive characters) in just a week of serious effort.
Speed and fluency can be achieved with about 6 weeks of regular practice.
You already have a head start on this, since you can recognize cursive characters with some effort. You merely need to achieve fluency. Fluency does not come from recognizing individual letters, but from recognizing patterns that form words or phrases.
Simply trying to read and grade the student papers is not sufficient to let you learn quickly. In fact, if it leads to frustration it will actually slow down the process of gaining fluency. Instead, you must engage in a regular (daily) program in which you repeatedly examine words and phrases written in cursive and attempt to guess (recognize) their meaning, then check the result and give yourself positive reinforcement for correct answers. The use of flash cards is one traditional way of doing this; phone apps are a modern alternative.
Here's one tried and true approach that I guarantee will work: Scan or photocopy a student paper and separate it into words and short phrases. Paste (or print out) each of these words or phrases on a flashcard, and on the other side of the card print the corresponding word or phrase in block letters or some other form that you can read fluently.
On the "answer" side of the cards, don't try to match the cursive word or phrase character by character. This is all about helping your brain map a new symbol (the cursive word or phrase) to its conceptual meaning. You can write the meaning in another language if you wish. In fact, another language will work better if it's more natural for you. Make one extra card that says "FINISHED!" or has a picture of something you like.
Shuffle your deck of flash cards and put the "FINISHED" card on the bottom, then look at the card on the top and try to guess the meaning. Don't agonize or try to decipher it letter-by-letter. Instead, just make a quick guess as to the meaning.
Turn the card over and look at the answer. If you were correct, give yourself a physical pat (somewhere on your body) and put the card on the bottom of the deck, below the "FINISHED" card. If you were wrong, put the card somewhere in the middle of the deck.
Give yourself a faster-than-comfortable time limit for each guess, so you are always feeling a little bit rushed for time and thus have a sense of urgency. You can use a timer or just push yourself on time.
Several times each day, take out the cards and go through them. When you can go through the entire deck and get to "FINISHED" without ever having to put any cards in the middle, you will be well on your way to fluency in reading cursive writing (or as most of the world calls it, 'handwriting').
You can add cards to the deck (or remove cards you have mastered) at any time. Handwriting style varies quite a bit from era to era, country to country, and person to person, so you will want to include a variety of handwriting samples over time. The inclusion of a surprisingly small number of variations will allow your brain to generalize its cursive pattern-recognition networks.
This approach works quickly to produce recognition fluency and is very resilient under variation in cursive writing style and the incorrect word spellings and other errors that often appear in handwritten material.
If you choose to pursue this approach, please come back here after a few weeks and tell us about your experience in achieving fluency!
Best of luck!