A table not covered with a tablecloth, and likewise a kitchen counter: if one of these got dirty, then the rule is:
If the dirty area is dry, one may clean it with a dry rag of any material, and may even rub with the dry rag in order to remove the food leftovers that are stuck. But it's impermissible to clean it with a damp or wet rag, as such use will perforce lead to squeezing out.
If the table or counter is damp, one may clean it with a nonabsorbent rag of synthetic material. He may, for the purpose of cleaning, even pour water on the table or counter, rub the dirt from it with his hand or a synthetic nonabsorbent rag, and even use a squeegee designated for [cleaning such surfaces]. But he should not clean the damp table or damp counter with a regular rag, even if [the latter] is dry.
―Sh'miras Shabas K'hilchasah 12:40; my own translation.
If the wipes you refer to are synthetic and nonabsorbent, it seems you can use them even with application of pressure. Otherwise, it seems you can't use them at all. But consult your rabbi.
Note also that there are many synthetic nonabsorbent brushes and scrub pads on the market. Consult your rabbi about their use (which, note, is not explicitly permitted by the SSK I quite above).