Of course, it's safe if the whole thing works on the new device, in fact you made a wallet/s recovery and the old laptop can only represent an additional risk. In case you plan to sell or give that old laptop to someone, I would suggest that you format the disk and maybe even try to use some additional tools that can almost completely erase the data from the disk. I usually never sell or give away such sensitive things, regardless of all methods, today's technology can save data even from disks that look completely destroyed to someone.

The good old method is still physical destruction by breaking the disc into pieces (use protective equipment), then douse it with some flammable liquid and set it on fire, and scatter the remains in a landfill.