The Collaborative International Dictionary of English v.0.48:

Squeamish \Squeam"ish\ (skw[=e]m"[i^]sh), a. [OE. squaimous,
   sweymous, probably from OE. sweem, swem, dizziness, a
   swimming in the head; cf. Icel. sveimr a bustle, a stir,
   Norw. sveim a hovering about, a sickness that comes upon one,
   Icel. svimi a giddiness, AS. sw[imac]ma. The word has been
   perhaps confused with qualmish. Cf. Swim to be dizzy.]
   Having a stomach that is easily turned or nauseated; hence,
   nice to excess in taste; fastidious; easily disgusted; apt to
   be offended at trifling improprieties.
   [1913 Webster]

         Quoth he, that honor's very squeamish
         That takes a basting for a blemish.      --Hudibras.
   [1913 Webster]

         His muse is rustic, and perhaps too plain
         The men of squeamish taste to entertain. --Southern.
   [1913 Webster]

         So ye grow squeamish, Gods, and sniff at heaven. --M.
                                                  Arnold.
   [1913 Webster]

   Syn: Fastidious; dainty; overnice; scrupulous. See
        Fastidious.
        [1913 Webster] -- Squeam"ish*ly, adv. --
        Squeam"ish*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

squeamishly
    adv 1: in a squeamish manner; "`I would rather not touch,' he
           said squeamishly"