There will be no holes in the frame to install the old hitch. The holes come in if you decide to let them install the friction sway control bar. If you are comfortable towing without the sway control bar then you might try it that way.
Your old hitch should fit just fine on the underslung coupler that Jayco uses. Might have to turn you shank over and remount the hitch head to accommodate it but it should be no problem.
If you are towing the new trailer for a long distance then I think I would purchase the Equal-i-zer hitch and bring it with you and let them install it - even if it costs a few pennies to do so. Then, when you get it home you can re-do the installation yourself to correct any deficiencies if any.
I don't think I would tow it without sway control unless you only have a short distance to go and at fairly slow speeds. If you have a bunch of freeway driving to do then I would use some kind of sway control. Using the friction control will mean drilling 6 holes into the A frame for the small ball. Using the Equal-i-zer or Blue Ox will not require any holes to be drilled.
If it were me, I would go with the new hitch. That
price at RVW with free shipping is very attractive! Just be aware that it does not include the ball. I would purchase
the ball from them and have them install it before shipping. DO NOT use the old ball from your old hitch if you get the Equal-i-zer. The shank length of the ball is too long for the hitch head and will hit the WD bars when turning. There is a special hitch ball for use with that hitch.
Barney