Activating part without resolving [[1]]

I'll try to make this question more clear in a little while. In the mean time, I'll ask directly the question which motivated it: Latin Square from submatrix

Original Question

I want, for instance, to obtain the code

{#[[1]],
 #2[[1]],
 #3[[1]],
 ...
 #999[[1]]}

and I'm not sure how to do it. If I run

Activate[Part[Inactive[Slot][#], 2] & /@ Range@999]

I get what I want, since Slot[n] has no second part. How do I get the input code for a part of an expression that may or may not exist without having it wrapped or inactive?

This problem arose when writing code to solve for missing matrix entries; each missing entry got assigned a numbered Slot. I may type this specific example up, but in the mean time here's a contrived example:

thelist=Table[#[[i]],{i,10}]&
(*Out[]={1,i[[2]],i[[3]],...,i[[10]]}*)

The desired output is

(*Out[]={i[[1]],i[[2]],i[[3]],...,i[[10]]}*)