Here's a solution. It's fully automatic and should well even for curved lines. The notation is avoid intersection={name of other path}{drawing options}. It finds the list of intersection points, then executes a decoration that measures the distance to the next intersection point and when gets close, does an evasive maneuver. Using the options avoid intersect amplitude, avoid intersect width, and avoid intersect offset you can adjust the evasive maneuver.

It's not perfect. It is very slow (on my computer, the two examples take 1.4 seconds and 3.8 seconds respectively), which may be unavoidable. Also, if you include the smooth option in the second example below it breaks with a "dimension too large" error. I have no idea why. I think the output looks very good.

documentclass{article}
usepackage{tikz}
usetikzlibrary{decorations}
usetikzlibrary{intersections}

makeatletter
tikzset{
  avoid intersection amplitude/.store in=avint@amplitude,
  avoid intersection width/.code={edefavint@width{dimexpr#1/2}},
  avoid intersection offset/.store in=avint@offset,
  avoid intersection has corners/.code={pgfdecoratepathhascornerstrue}
}
defavint@amplitude{5pt}
defavint@width{5pt}
defavint@offset{0pt}

pgfdeclaredecoration{avoidintersect}{initial}{
  state{initial}[width=pgfdecoratedinputsegmentlength/100,next state=measure]
  {
    gdefavint@intersectionnumber{1}
    pgfpathlineto{pgfpointorigin}
  }

  state{measure}[width=pgfdecoratedinputsegmentlength/100,next state=wait,auto corner on length=2pt,
               persistent postcomputation=letpgf@decorate@next@stateavint@smuggle@pgf@decorate@next@state]
  {
    pgfpathlineto{pgfpointorigin}
    pgfgettransformavint@temptransform
    pgftransforminvert
    pgfpointintersectionsolution{avint@intersectionnumber}
    pgf@pos@transform{pgf@x}{pgf@y}
    pgfmathveclen{pgf@x}{pgf@y}
    pgfsettransformavint@temptransform
    xdefavint@waitcycles{thenumexprdimexprpgfmathresult pt-avint@width*3-avint@offsetrelax/dimexprpgfdecoratedinputsegmentlength/100relax}
    ifnumavint@waitcycles>50relaxgdefavint@waitcycles{50}fi
    globalletavint@smuggle@pgf@decorate@next@statepgf@decorate@next@state        
    ifdimpgfmathresult pt<dimexpravint@width+avint@offsetrelax
        gdefavint@smuggle@pgf@decorate@next@state{zig}
    else
        ifdimpgfmathresult pt<dimexpravint@width*2+avint@offsetrelax
            gdefavint@smuggle@pgf@decorate@next@state{measure}    
        fi
    fi        
  }

  state{wait}[width=pgfdecoratedinputsegmentlength/100,next state=measure,repeat state=avint@waitcycles,auto corner on length=2pt]{
    pgfpathlineto{pgfpointorigin}
  } 

  state{zig}[width=avint@width, next state=zag]{
    pgfpathcurveto{pgfqpoint{avint@width}{0cm}}{pgfqpoint{0pt}{avint@amplitude}}{pgfqpoint{avint@width}{avint@amplitude}}
  }
  state{zag}[width=avint@width, next state=measure,
              persistent postcomputation=letpgf@decorate@next@stateavint@smuggle@pgf@decorate@next@state]{
    pgfpathcurveto{pgfqpoint{avint@width}{avint@amplitude}}{pgfqpoint{0pt}{0cm}}{pgfqpoint{avint@width}{0pt}}
    xdefavint@intersectionnumber{thenumexpravint@intersectionnumber+1}
    globalletavint@smuggle@pgf@decorate@next@statepgf@decorate@next@state
    ifnumavint@intersectionnumber>pgfintersectionsolutions
      gdefavint@smuggle@pgf@decorate@next@state{done}
    fi
  }

  state{done}[width=pgfdecoratedinputsegmentlength/100,auto corner on length=2pt]{
    pgfpathlineto{pgfpointorigin}
  }

  state{final}{pgfpathlineto{pgfpointdecoratedpathlast}}
}    

tikzset{
    avoid intersection/.code 2 args={
        pgfkeysalso{name path=avint@temp,draw=none}
        expandafterdefexpandaftertikz@postactionsexpandafter{tikz@postactions
            pgfintersectionsortbyfirstpath
            tikz@intersect@namedpaths
            pgfintersectionofpaths
                {pgfsetpathtikz@intersect@path@name@avint@temp}
                {expandafterpgfsetpathcsname tikz@intersect@path@name@#1endcsname}
            begin{pgfdecoration}{{avoidintersect}{pgfdecoratedpathlength}}
            pgfsetpathtikz@intersect@path@name@avint@temp
            end{pgfdecoration}
            pgfgetpathavint@temp@path
            pgfusepath{discard}
            draw[/utils/exec={tikz@addmode{pgfsyssoftpath@setcurrentpathavint@temp@path}},#2](0,0)rectangle (0,0);%
        }
    }
}
makeatother

begin{document}
begin{tikzpicture}
    coordinate (a) at (-1,0.5);
    coordinate (b) at (8,0.5);
    coordinate (c) at (3,-0.5);
    draw[ultra thick, name path=sine, domain=-1:8, smooth, samples=50] plot (x,{sin(x r)});
    draw[avoid intersection={sine}{white,double=black},avoid intersection has corners] (a) -- (c) |- (b);
end{tikzpicture}

begin{tikzpicture}
    coordinate (a) at (-1,0.5);
    coordinate (b) at (8,0.5);
    coordinate (c) at (3,-0.5);
    draw[ultra thick,name path=line] (a) -- (c) |- (b);
    draw[avoid intersection={line}{white,double=black},avoid intersection offset=1.5pt,domain=-1:8,samples=50] plot (x,{sin(x r)});
end{tikzpicture}

end{document}

Here's the output:

You can see that the line join works fine: