Shader - Remove Alpha before adding color

Hello, I am new to shaders and I am taking a shot out creating one. My idea is that the model itself would be invisible, but a rim around the model would glow. The problem that I am having is that reducing the alpha to zero makes both the model AND the emission dissapear. How do I make the model dissapear but leave the emmisive? Here is my shader:

SubShader {
		Tags { "Queue"="Transparent" "RenderType"="Transparent" }
		LOD 200
		
		CGPROGRAM
		#pragma surface surf Lambert alpha

		struct Input {
			float3 viewDir;
			float2 uv_Maintex;
		};
		
		float4 _RimColor;
		float _RimPower;
		sampler2D _MainTex;

		void surf (Input IN, inout SurfaceOutput o) {
		    o.Alpha = 0;
		    
			half rim = 1.0 - saturate(dot(normalize(IN.viewDir), o.Normal));
			o.Emission = _RimColor.rgb * pow(rim, _RimPower);
		}
		ENDCG
	}

Thanks!

I solved it by doing this:

o.Alpha = 0;
		    
half rim = 1.0 - saturate(dot(normalize(IN.viewDir), o.Normal));
o.Emission = _RimColor.rgb * pow(rim, _RimPower);
o.Alpha = pow(rim, _RimPower) * _Opacity;