OP - semi-horizontal is not horizontal. It looks like you have basic nothing-special aluminum skewers. Replacing them with PitLocks would be an upgrade. No problem. Just be sure to seat the axle back in the slot (I trust you displaced it for the photo)
In general, though you can do it, (and as AEO notes there are QR skewers and there are QR skewers), you're in a danger zone [using skewers with horizontal drops or track ends]. See the note at the end of Peter White's
treatise on PitLocks.
I don't recommend a Pitlock rear skewer if your frame has horizontal dropouts. Horizontal dropouts require very high clamping force, otherwise the wheel will slip forward in the right dropout. Pitlocks are designed for vertical dropouts, which do not require high clamping force. The Pitlocks can't produce enough clamping force for a horizontal dropout. Think of them as comparable to aluminum QR skewers, which, as most people now know, can't be used with older bikes having horizontal dropouts. But with vertical dropouts, Pitlocks will hold your wheel quite securely in the frame. Don't worry.
The earlier question re (paraphrased) "does frame material, aluminum vs. steel, matter re skewers on horizontal dropouts" -- absolutely not. There is a slight difference in the friction and compressibility of the two materials, but the issue is that a QR skewer generates all the clamping force by the tension in the relatively thin skewer, while a non-QR uses the beefy threaded axle and nuts. It's the configuration of the clamping hardware, not the dropout material being clamped, that matters. Horizontal drops and track ends require a more bodacious clamping force because the dropout isn't helping any.
And cross-check is pretty darn horizontal