You can use 1mM EDTA (or if really adherent, bump it up to 10mM). The EDTA will chelate the calcium and some metal ions which would lift the cells up without 'chopping' any proteins.
We usually use this for really fragile primaries, I would definitely play around with the incubation time (2 minutes to 10 in 37 degrees.), but it's usually less damaging than trypsin so you can incubate your cells a bit longer.
Hi Sharon, to avoid adherense to plastic cell culture flasks, you can change culture conditions and culture monocytes i cell culture bags (e.g.Veu Life CellGenix). This procedure will reduce the cell adherense.