The funds being made available for the TCX/Excel type schemes are being made available to you by HSBC through a loan negotiated by OATs. HSBC and Cabair have the same arrangements. If you are going to attend an integrated course at Cabair you can apply for the same loan just as you can at OATs. Also the amount required for the Flybe scheme is under the £40,000 cut off point at which HSBC start wanting hard guarantees (i.e your parents house). Below that amount they generally seem happy with a parents signature.
The Flybe scheme just hasn't done all the leg work for you and got the loan forms ready for you sign, you just have to prepare a simple business type plan and talk to HSBC yourself.
As for the Flybe guarantee, again its simply a parent's signature that is required if you have no major assets (ie a house) yourself.