No, it is not safe. A CRT is fundamentally a high-voltage device, and as such the operation of one requires circuitry to boost the external supply voltage to the orders of magnitude higher voltage required to actually accelerate electrons through the tube. In a properly engineered consumer product, all high voltage parts are safely out of reach inside, but in a surplus part used for experimentation that is not necessarily the case. Working with such requires orders of magnitude more awareness and expertise than demonstrated in the question.
For Arduino projects there are many inexpensive, compact, simple to apply OLED and LCD displays available. In contrast to a video display requiring rapidly and precisely timed repeating analog output, many have simple asynchronous digital interfaces such that you can draw your pixels once with I2C or SPI operations and they then continue to display while your code does something else.
If you really want to play with video generation circuitry, find a fully enclosed productized TV or ancient (Apple/Commodore/Atari style) monitor with composite RGB input, a VGA monitor with analog RGB input, or an oscilloscope with a Z axis input on the back and interact with it only via the provided input connectors without opening the case.