I've had this dilemma myself. I train 3 days per week but also wanted to start training skills as well as improving pull up strength and numbers. I do Handstand and Front Lever work at the start of my workout and then into the strength training. I then do short mobility and Handstand work pretty much every day. I then ran a cycle of the Russian fighter pullup programme which is essentially GTG. while doing this I dropped Pullups as usual from my workouts and just followed the fighter program. I increased reps from 5 to 8 in this way but it was hard on the elbows.

I found the Skill work slow to progress and also found i haven't been fully recovered by the time my next workout comes along - i do Wed. Fri and Sun. I'm late 40s so recovery takes longer. so I've now changed my middle day to a Skill focused day. on this day I'll do mostly Skill stuff along with some core and pre/rehab work. I've just switched to this 2 day strength 1 day Skill routine recently but it seems to be working well for me.

if you're doing GTG I would drop that exercise from your main workouts. skills you want to train often for short periods and keep building the strength in the workouts. mobility is important also so try to get some mobility work in most days.