Professional DJs used to be against this, but Key Lock (Master Tempo) in more recent CDJs has finally got good enough to not sound weird when you use it.
Anything from the CDJ-2000nxs1 onward (including XDJ-1000) got really good at not crushing the audio - meaning you can keep the key lock / master tempo on and move the tempo quite a bit (I often work around 2-6bpm with master tempo on)
Sometimes, however, certain tracks just are NOT going to sound right beyond 2 or 3bpm. In layman’s terms the kick drum may sound like it’s actually being fast forwarded (among other weird sounds), you will notice something not sounding ‘right’ but that’s relatively rare and you would hear it in the headphones and move on to the next track.
Old school vinyl DJs I know did used to write the BPM on the vinyl but they were working with really old technology in the 90s and 2000s.
I really wouldn’t worry about BPM in the
120 to 122 range or even up to the 125 or 128 personally. Most of it works.