How to draw a line on a mesh edge using a shader

I tried a lot of different options, like a outline, a wireframe shader, but they all do not give the desired effect.

 Shader "Custom/WireframeShader"
 {
     Properties
     {
         _WireColor("Edges Color", Color) = (0,0,0,1)
         _WireThickness("Edge Thickness", RANGE(0, 800)) = 100
         _WireSmoothness("Edge Smoothness", RANGE(0, 20)) = 3
         _AlbedoColor("Albedo Color", Color) = (1,1,1,1)
         _MainTex("Albedo (RGB)", 2D) = "white" {}
     }
 
         SubShader
     {
         Tags{ "RenderType" = "Opaque" }
         LOD 200
 
         Pass
     {
         CGPROGRAM
         // Use shader model 3.0 target, to get nicer looking lighting
 #pragma target 3.0
 
 #include "UnityCG.cginc"
 
 #pragma vertex vert
 #pragma fragment frag
 #pragma geometry geom
 
         uniform sampler2D _MainTex;
     uniform float4 _MainTex_ST;
 
     struct Input
     {
         float2 uv_MainTex;
     };
 
     fixed4 _WireColor;
     fixed4 _AlbedoColor;
 
     uniform float _WireThickness;
     uniform float _WireSmoothness;
 
     struct appdata
     {
         float4 vertex : POSITION;
         float2 texcoord0 : TEXCOORD0;
         UNITY_VERTEX_INPUT_INSTANCE_ID
     };
 
     struct v2g
     {
         float4 projSpaceVertex : SV_POSITION;
         float2 uv0 : TEXCOORD0;
         float4 worldSpacePosition : TEXCOORD1;
         UNITY_VERTEX_OUTPUT_STEREO
     };
 
     struct g2f
     {
         float4 projSpaceVertex : SV_POSITION;
         float2 uv0 : TEXCOORD0;
         float4 worldSpacePosition : TEXCOORD1;
         float4 dist : TEXCOORD2;
         UNITY_VERTEX_OUTPUT_STEREO
     };
 
     v2g vert(appdata v)
     {
         v2g o;
         UNITY_SETUP_INSTANCE_ID(v);
         UNITY_INITIALIZE_VERTEX_OUTPUT_STEREO(o);
         o.projSpaceVertex = UnityObjectToClipPos(v.vertex);
         o.worldSpacePosition = mul(unity_ObjectToWorld, v.vertex);
         o.uv0 = TRANSFORM_TEX(v.texcoord0, _MainTex);
         return o;
     }
 
 
     [maxvertexcount(3)]
     void geom(triangle v2g i[3], inout TriangleStream<g2f> triangleStream)
     {
         float2 p0 = i[0].projSpaceVertex.xy / i[0].projSpaceVertex.w;
         float2 p1 = i[1].projSpaceVertex.xy / i[1].projSpaceVertex.w;
         float2 p2 = i[2].projSpaceVertex.xy / i[2].projSpaceVertex.w;
 
         float2 edge0 = p2 - p1;
         float2 edge1 = p2 - p0;
         float2 edge2 = p1 - p0;
 
         float area = abs(edge1.x * edge2.y - edge1.y * edge2.x);
         float wireThickness = 800 - _WireThickness;
 
         g2f o;
 
         o.uv0 = i[0].uv0;
         o.worldSpacePosition = i[0].worldSpacePosition;
         o.projSpaceVertex = i[0].projSpaceVertex;
         o.dist.xyz = float3((area / length(edge0)), 0.0, 0.0) * o.projSpaceVertex.w * wireThickness;
         o.dist.w = 1.0 / o.projSpaceVertex.w;
         UNITY_TRANSFER_VERTEX_OUTPUT_STEREO(i[0], o);
         triangleStream.Append(o);
 
         o.uv0 = i[1].uv0;
         o.worldSpacePosition = i[1].worldSpacePosition;
         o.projSpaceVertex = i[1].projSpaceVertex;
         o.dist.xyz = float3(0.0, (area / length(edge1)), 0.0) * o.projSpaceVertex.w * wireThickness;
         o.dist.w = 1.0 / o.projSpaceVertex.w;
         UNITY_TRANSFER_VERTEX_OUTPUT_STEREO(i[1], o);
         triangleStream.Append(o);
 
         o.uv0 = i[2].uv0;
         o.worldSpacePosition = i[2].worldSpacePosition;
         o.projSpaceVertex = i[2].projSpaceVertex;
         o.dist.xyz = float3(0.0, 0.0, (area / length(edge2))) * o.projSpaceVertex.w * wireThickness;
         o.dist.w = 1.0 / o.projSpaceVertex.w;
         UNITY_TRANSFER_VERTEX_OUTPUT_STEREO(i[2], o);
         triangleStream.Append(o);
     }
 
     fixed4 frag(g2f i) : SV_Target
     {
         float minDistanceToEdge = min(i.dist[0], min(i.dist[1], i.dist[2])) * i.dist[3];
 
     float4 baseColor = _AlbedoColor * tex2D(_MainTex, i.uv0);
 
     // Early out if we know we are not on a line segment.
     if (minDistanceToEdge > 0.9)
     {
         return fixed4(baseColor.rgb,0);
     }
 
     // Smooth our line out
     float t = exp2(_WireSmoothness * -1.0 * minDistanceToEdge * minDistanceToEdge);
     fixed4 finalColor = lerp(baseColor, _WireColor, t);
     finalColor.a = t;
 
     return finalColor;
     }
         ENDCG
     }
     }
         FallBack "Diffuse"
 }

For example, such a shader gives the following result:

How can I leave only the outer edges of the mesh?