Tcl, 84 bytes

With renaming allowed, things get shorter:

file rename i.txt m file rename -force o.txt i.txt file rename m o.txt file delete m 

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set A [read [open i.txt]] puts [set i [open i.txt w]] [read [open o.txt]] puts [set o [open o.txt w]] $A close $i close $o 

Tcl, 71 bytes

file ren i.txt m file ren -force o.txt i.txt file ren m o.txt file de m 

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file rename i.txt m file rename -force o.txt i.txt file rename m o.txt file delete m 

set A [read [open i.txt]] puts [set i [open i.txt w]] [read [open o.txt]] puts [set o [open o.txt w]] $A close $i close $o 

Tcl, 122 bytes

set A [read [open i.txt]] puts [set i [open i.txt w]] [read [open o.txt]] puts [set o [open o.txt w]] $A close $i close $o 

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Tcl, 84 bytes

With renaming allowed, things get shorter:

file rename i.txt m file rename -force o.txt i.txt file rename m o.txt file delete m 

Try it online!

set A [read [open i.txt]] puts [set i [open i.txt w]] [read [open o.txt]] puts [set o [open o.txt w]] $A close $i close $o 

Tcl, 122 bytes

set A [read [open i.txt]] puts [set i [open i.txt w]] [read [open o.txt]] puts [set o [open o.txt w]] $A close $i close $o 

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---

set A [read [set i [open i.txt r]]] set B [read [set o [open o.txt r]]] close $i close $o puts [set i [open i.txt w]] $B puts [set o [open o.txt w]] $A close $i close $o 

Tcl, 122 bytes

set A [read [open i.txt]] puts [set i [open i.txt w]] [read [open o.txt]] puts [set o [open o.txt w]] $A close $i close $o 

Try it online!