You can use just witch hazel but it's "oil control" properties are no-where near that of a proper alcohol based splash, though if you had no other choice you could use just witch hazel in a pinch. I'm not sure why you feel that an alcohol based splash will cause more oil... You'll have to really just have first hand experience. Use this as an example: when a teenager gets acne on their face it is caused by over active/productive oil glands, so they use astringents and or toners that, while having other ingredients, are primarily alcohol and/or witch hazel. Treat your head like the face of a teenager and your issue should minimalize if not disappear entirely.
As for my shaving cream/soaps of choice:
I regularly alternate between proraso green cream and a la toja shave stick, both used with an omega synthetic brush. I also have a new maggard synthetic brush on the way but that is another post for another time. In terms of efficacy the proraso and the la toja both lather like a dream and offer AMAZING shaves so for me it really comes down to a scent difference and what I'm in the mood for at the time. Since the la toja is a stick, it's extreme ease of use (just wet your head, rub it around, then work up lather with brush directly on skin) and portable size may give it a slight advantage. Both are considered wet shaving staples though and I suggest trying them both if you venture into proper wet shaving.
I also have a col conk lime scented glycerin soap that I melted into a shave stick. I'm not sure about that stuff... Very little cushion but a very "sticky" slickness and minimal protection. That was a cheap soap I wanted to try for fun. In this same category I have a puck of van der hagen deluxe which offers much more cushion and protection then the col conk line glycerin however it still comes nowhere near the la toja or proraso.
If time is an issue or I don't feel like busting out the whole brush and soap combo then I'll use gillette foamy menthol. This stuff is a staple around my home. Say what you want about canned foo, this stuff is legit. It smells and feels great, offers nice protection, doesn't contribute to skin oil production, and is quick. As long as gillette doesn't discontinue this there will always be a can in my home. My wife also uses it daily for her needs. Last but not least, headslick. I have a love/hate relationship with this stuff. I get a great first pass but then subsequent passes always seems to drag and pull. Probably the least used product of the ones I have.