You can use variables in the replay script as a means to parameterize edge parameters. Here is an example:

#variables
set n 10
set h1 0.01
set r1 1.2
ic_load_tetin myfile.tin
ic_hex_surface_blocking -inherited -swept -min_edge 0.0
ic_geo_new_family SOLID
ic_hex_twod_to_threed SOLID -swept
ic_hex_set_mesh 19 18 n $n h1 $h1 h2rel 0.0 r1 $r1 r2 2 lmax 0 default unlocked
ic_hex_create_mesh SURFS SOLID proj 2 dim_to_mesh 3
ic_hex_write_file hex.uns SURFS SOLID proj 2 dim_to_mesh 3 -family_boco family_boco.fbc
ic_uns_load hex.uns 3 0 {} 2

The variables for the edge parameters are set at the top of the replay file. Within the script, the '$' indicates a variable. To parameterize the edge parameters, you can update the variables at the top of the script and then rerun the script.