I'm sure Ubuntu will work well for you, as would many other modern Linux distros. But before you begin, I would suggest that you make a "HP Recovery Set" (DVD or USB) of your Windows 10 so you could return to it later if you want. There is usually a program built in that will make the Recovery set for you. This process can awhile, even on USB. I just made a Recovery for my wife and it took about 2 hours.
I'm not sure what you mean by "secure boot." Do you mean that you want the UEFI Secure Boot feature to remain working? Ubuntu may install with Secure Boot enabled... some distros can. But some will need Secure Boot disabled in UEFI settings or they won't work. So just leave it enabled if it works, or disable it if it doesn't. Also in UEFI settings, you will probably need to disable Fast Boot, if you see that in there.
If you just mean you want Ubuntu to be secure once you have it installed, be assured it will be. It will be much more secure than Windows, in my opinion. You might check that your firewall (ufw usually) is enabled.
If you are able to boot on the Ubuntu USB okay, then it will probably install okay and boot from your laptop. But you may run into some issues to work out. For example, I'm not sure how Ubuntu will see the internal flash drive versus a regular hard drive. In the install process you will have to identify that, and tell it to put the GRUB bootloader on it. This may work automatically, or you may have to manually set up partitions... including an EFI partition to put the bootloader into. If you don't get it right the first time, try again a little differently and you'll probably get it.