To be clear, Texture2D::Load is functionally equivalent to using the [] operator. They're just different HLSL syntax that compiles to the same exact bytecode.
The way that they both work is that they use unnormalized coordinates to access the texture data. So for a 2D texture you'll typically pass a pair of integers where the X component is of the range [0, width - 1] and the Y component is of the range [0, height - 1] (values outside of that range will always return 0). This is different from the normalized UV coordinates that are used for Texture2D::Sample, where you pass [0.0, 1.0] floats that are mapped to the minimum and maximum extents of the texture. To convert from normalized to unnormalized coordinates you can use some simple math:
int2 unNormalized = int2(uv * float2(textureWidth, textureHeight));
Hopefully this makes it clear that you can pass arbitrary coordinates to Load or operator[], and so there's no requirement that the texture you're sampling has dimensions that exactly match the dimensions of your render target. However you may have to do a bit of math to compute the coordinates that you pass.
So what Mercasa suggested was using "myTex[uint(svPosition) % textureSize]", which is one way of mapping your texture to your pixel shader positions. What this will do here is essentially "tile" the low-resolution texture across your larger-resolution render target. So for instance if the low-resolution texture is 1/4 the width and height of your render target, the low-resolution render target will repeat 4 times in the X direction and 4 times in the Y direction, effectively "repeating' it 16 times total. I suspect what you want is to instead load your texture such that the low-resolution texture still "covers" the same amount of screen space as the source texture and effectively covers the entire output render target. So if it was 1/4 the width and height, each texel of the low-res texture would cover a 4x4 block of pixels being shaded by your pixel shader. To do this, you'll want to divide the pixel coordinate by your "k" factor, where rtSize / textureSize == k:
myTex[uint2(svPosition / k)]
Doing this will be roughly equivalent to using Sample with normal screen-mapped UV coordinates, with point filtering applied.