To deactivate the information on client side, that the used browser is not a member of the list of supported browsers for WebOffice 10 R3, you can customize the file <WebOffice installation directory>\client\JSX\js\JSX30.js.
Note: Adapting the JSX30.js file only causes the deactivation of the warning message for not supported browsers. It is not possible to add new browsers and have warning messages displayed for them.
The default setting is to present this alert when accessing WebOffice 10 R3 with Google Chrome or Safari.
jb._D={
ie6:[ub.q,[ub.nd,ub.rd,ub.sd],ub.td,6],
ie7:[ub.p,[ub.nd,ub.ud,ub.sd],ub.td,7],
ie8:[ub.p,[ub.nd,ub.vd,ub.sd],ub.td,8],
ie9:[ub.p,[ub.nd,ub.wd,ub.sd],0,9],
fx1_5:[ub.B,[ub.xd,ub.yd,ub.zd],ub.td,1.5],
fx2:[ub.B,[ub.xd,ub.Ad,ub.yd,ub.zd],ub.td,2],
fx3:[ub.B,[ub.xd,ub.Bd,ub.yd,ub.zd],ub.td,3],
fx4:[ub.B,[ub.xd,ub.Cd,ub.yd,ub.zd],0,4],
gc1:[ub.Dd,[ub.Ed,ub.Fd,ub.yd,ub.Gd,ub.Hd],0,3],
sf3:[ub.Dd,[ub.Ed,ub.Fd,ub.yd,ub.Gd],ub.td,3],
sf4:[ub.Dd,[ub.Ed,ub.Id,ub.yd,ub.Gd],0,4],
op9:[ub.A,[ub.Jd],0,9],
op10:[ub.A,[ub.Jd],0,10],
ie:[ub.A,[ub.nd,ub.rd,ub.sd]],
fx:[ub.B,[ub.xd,ub.yd,ub.zd]],
sf:[ub.Dd,[ub.Ed,ub.yd,ub.Gd]],
op:[ub.A,[ub.Jd]],
gk:[ub.B,[ub.xd,ub.yd,ub.zd]],
xx:[ub.B,[]]};

Unsupported browser information starting WebOffice using Google Chrome
You can change this setting by entering the string ub.td inside the brackets (pre-last position) of the concerning browsers. For Google Chrome and Safari 4 this would be:
ie6:[ub.q,[ub.nd,ub.rd,ub.sd],ub.td,6],
ie7:[ub.p,[ub.nd,ub.ud,ub.sd],ub.td,7],
ie8:[ub.p,[ub.nd,ub.vd,ub.sd],ub.td,8],
ie9:[ub.p,[ub.nd,ub.wd,ub.sd],0,9],
fx1_5:[ub.B,[ub.xd,ub.yd,ub.zd],ub.td,1.5],
fx2:[ub.B,[ub.xd,ub.Ad,ub.yd,ub.zd],ub.td,2],
fx3:[ub.B,[ub.xd,ub.Bd,ub.yd,ub.zd],ub.td,3],
fx4:[ub.B,[ub.xd,ub.Cd,ub.yd,ub.zd],0,4],
gc1:[ub.Dd,[ub.Ed,ub.Fd,ub.yd,ub.Gd,ub.Hd], ub.td,3],
sf3:[ub.Dd,[ub.Ed,ub.Fd,ub.yd,ub.Gd],ub.td,3],
sf4:[ub.Dd,[ub.Ed,ub.Id,ub.yd,ub.Gd], ub.td,4],
op9:[ub.A,[ub.Jd],0,9],
op10:[ub.A,[ub.Jd],0,10],
ie:[ub.A,[ub.nd,ub.rd,ub.sd]],
fx:[ub.B,[ub.xd,ub.yd,ub.zd]],
sf:[ub.Dd,[ub.Ed,ub.yd,ub.Gd]],
op:[ub.A,[ub.Jd]],
gk:[ub.B,[ub.xd,ub.yd,ub.zd]],
xx:[ub.B,[]]};

Opened project with Google Chrome
Note: Backup your changes, because they may be affected by patches and updates!