Like your design!
To make it the size you want without sashing would require 17 or 18 inch blocks depending on the width of border you want.
18 x 5 = 90 + 3"(x2) border = 96
17 x 5 = 85 + 6.5"(x2) border (or multiple borders to get this width)
18 x 7 = 126 (bigger than you want, even without border)
17 x 7 = 119 (still bigger than you want)
Well let's see what we get with 16" blocks...
16 x 5 = 80 so would need 8"(x2) of border on this dimension
16 x 7 = 105 but 8"(x2) of border here gives you 121"
15.5 x 5 = 77.5 so would need 11.25"(x2) of border
15.5 x 7 = 108.5 only need 1.5 inches total here
If you changed it to 7 x 9 (keeping to the odd# of squares each way, which I think is the effect you're aiming for) let's see what we get...
13 x 7 = 91 so 2.5"(x2) border to get 96"
13 x 9 = 97 so 2.5"(x2) border gives you 102" meaning you would need a second 4"(x2) border in this dimension
or
12 x 7 = 84 so 6" (x2) of border gives you 96"
12 x 9 = 98 and 6" (x2) of border would give you 110"
Hope this helps!