Well, this MASSIVELY changes the hint. Lack of options while recovering is the biggest change here, if you ask me. If you combine this with the "problems killing may keep this character from being too good", it eliminates most of the characters who have trouble killing: Pit, ZSS, and Sheik all have versatile recoveries.
I'd definitely say Lucario now. On most of the stages, Wall Clinging is not an option, leaving only the Up B, which has a lot of landing lag and no attack, making it easily edge-hogged and easily punished on the stage. His highest power killing moves (his smashes) are insanely laggy.
Alternately, this could be Sheik now. The Tether, wall cling, and Vanish give some variety to the recovery, but usually if any of the techniques could get Sheik back, they all could. Sheik's three best KO moves (upsmash, forward smash, and Vanish) are pretty much the only three moves in Sheik's arsenal with any lag on them. And Sheik is VERY capable of turning a match around from behind. Sometimes the combos just flow out, and your opponent has suddenly taken Double-Jab cancelled into Forward Tilt into a 4+ hit Forward Tilt Chain into an Uptilt into a Walking Forward Tilt into another Forward Tilt Chain into a Tippered Upsmash or Double-Hit Upsmash for a nice whopping 90%+ out of nowhere. And with judicious use of the Back Air, Up Tilt, Down Smash, Needles, and Grabs, Sheik can play a defensive harassment game that will pressure the opponent and rack up damage without much possibility of retaliation.
Especially the part about Shield pressure seems very much Sheik. Sheik can do something like a Fair/Nair/Bair into Double-Jab cancelled into a Ftilt, and at proper spacing this will be ungrabable by most characters and will put a ton of pressure on the Shield.