After (minimal) testing, it seems cursor keys don't trigger INKEY$ even in own window (in shell console indeed is in cooked mode), so I don't think you can read the cursor keys with ace.
testing program follows
Code:
defint a-z
screen 1,320,200,3,1
palette 0,0,0,0
palette 1,0,0,1
palette 2,0,1,0
palette 3,0,1,1
palette 4,1,0,0
palette 5,1,0,1
palette 6,1,1,0
palette 7,1,1,1
window 1,"Hello World! <press 'q' key to quit>",(0,0)-(320,200),32,1
c$=""
while c$<>"q"
c$=""
while c$=""
sleep
c$=inkey$
wend
x=rnd*80
y=rnd*25
repeat
f=rnd*7+1
b=rnd*8
until f <> b
color f,b
locate y,x
print asc(c$);
wend
window close 1
screen close 1