If you want to crossup, j.mk as usual for the safe jump.
If you don’t want to crossup, use j.lk for the safe jump (super long active frames… use it early if you want to… all you need to time is when you jump. No so much when to press the lk).
And really. Safe jumping is the important thing to retain here. I’ve heard people saying several times that certain characters can’t be jumped on, on wake up. Well, every single one of them is. All you need to know is the startup frames on their reversals.
Also, get used to only doing safe jumps on untechable knockdowns that give you enough time to pull off a safe jump (you rather land early and whiff your jumping attack, than pull that attack off, and be too late, eating an SRK).
SRK has 2 frames for startup, active on the 3rd (3 frames startup as people call it). You have to land in 2 frames after using your Jumping attack and BE BLOCKING. Not an easy task, but that’s what training mode is for.
To practise it, grab ryu on the 1P side, grab deejay on the 2P side.
Record deejay doing his close throw on ryu (so ryu lands closest to him), or c.mk sweep him. Then try a safe jump on him (remember to keep your block ready during the jump).
To make sure you did it well, put it on playback, let Deejay sweep/throw you, and then do a reversal shoryuken with ryu. If you did it right, deejay’s attack will whiff through the first 2 frames of the shoryuken (invencibility) and he’ll land crouch blocking. Free punish.
Shoryukens are the worst case scenario. After you record a successful safe jump, you’re free to pick different 1P characters and still keep 2P Deejay on playback (it’ll be saved as long as you don’t leave training mode other than to choose different characters).
Try it on “supposedly impossible to jump on characters”. Like Gief using KKK Lariet, or Blanka using LP electricity (smallest startup-> 4 frames, active on 5th). It’ll stuff them.
Against most characters it’s not worth risking a c.lk or c.lp after a safe jump. If it’s blocked, they can reversal you, and a character like gief can easily SPD you. Just use safe jumps as a kind of mixup. Most of the time, people will try to reversal you. If they’re not reversal happy in the first place, or if they figure out that you’re doing some “Magical Jump that apparentely can’t get hit”, then you may start doing some followups. I prefer to use safe jumps, delay, and try a throw, or do a backdash.
Also, read their EX meter.
Certain characters are free on wakeup because after a safe jump, you can still do a followup on block and not be reversal’d (specially since safe jumps are so LATE, that the blockstun itself allows jabs and shorts to followup without a reversal breaking in). Rufus is free without EX meter. So is Dictator if you can OS or simply read his Teleport. So is Zangief (I wouldn’t risk it, just in case you mistime the safe jump, it whiffs, and you land without blockstun on him).
Long story short, there is no “safe” mixup routine after a knockdown. It’s very character specific. On some characters, it’s pretty free to just safe jump, c.short > throw, or hit confirm it into another sweep (or EX machine gun, dash ultra2). Against others, not so much. Keep it safe.